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Published online by Cambridge University Press:  15 November 2019

Amnon Yekutieli
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Ben-Gurion University of the Negev, Israel
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Derived Categories , pp. 590 - 599
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References

Alonso, L., Jeremias, A. and Lipman, J., Local homology and cohomology on schemes, Ann. Sci. ENS 30 (1997), 139. Correction www.math.purdue.edu/~lipman.Google Scholar
Altman, A. and Kleiman, S., A term of commutative algebra, http://web.mit.edu/18.705/www.Google Scholar
Angeleri Hügel, L., Happel, D. and Krause, H. (eds.), Handbook of Tilting Theory, London Math. Soc. Lecture Note Ser. 332 (2006), 147173.Google Scholar
Arinkin, D. and Bezrukavnikov, R., Perverse coherent sheaves, Mosc. Math. J. 10 (2010), 329.Google Scholar
Artin, M., Grothendieck, A. and Verdier, J.-L., (eds.), Séminaire de Géométrie Algébrique du Bois Marie – 1963-64 – Théorie des Topos et Cohomologie Étale des Schémas, SGA 4, vol. 1, Lecture Notes in Mathematics 269, Springer, 1972.Google Scholar
Artin, M. and Schelter, W., Graded algebras of dimension 3, Adv. Math. 66 (1987), 172216.Google Scholar
Artin, M., Small, L. W. and Zhang, J. J., Generic flatness for strongly noetherian algebras, J. Algebra 221 (1999), 579610.CrossRefGoogle Scholar
Artin, M., Tate, J. and Van den Bergh, M., Some algebras associated to automorphisms of elliptic curves, in The Grothendieck Festschrift, Vol. I, Birkhäuser, 1990, pp. 3385.Google Scholar
Artin, M., Tate, J. and Van den Bergh, M., Modules over regular algebras of dimension 3, Invent. Math. 106 (1991), 335388.Google Scholar
Artin, M. and Zhang, J. J., Noncommutative projective schemes, Adv. Math. 109 (1994), 228287.Google Scholar
Auslander, M., Platzeck, M. and Reiten, I., Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979), 146.Google Scholar
Avramov, L. L., Infinite free resolutions, in Six Lectures on Commutative Algebra, Elias, J. et al., (eds.), Birkhäuser, 1998, pp. 1118.Google Scholar
Avramov, L. L., Iyengar, S. B. and Lipman, J., Reflexivity and rigidity for complexes, I: Commutative rings, Algebra Number Theory 4 (2010), 4786.Google Scholar
Avramov, L. L., Iyengar, S. B., Lipman, J. and Nayak, S., Reduction of derived Hochschild functors over commutative algebras and schemes, Adv. Math. 223 (2010) 735772.CrossRefGoogle Scholar
Beilinson, A. A., Coherent sheaves on Pn and problems in linear algebra, Funktsional Anal. i Prilozhen. 12 (1978), 6869 (Russian). English translation in Functional Anal. Appl. 12 (1978), 214–216.Google Scholar
Beilinson, A. A., Bernstein, J. and Deligne, P., Faisceaux pervers, Astérisque 100, 1980.Google Scholar
Berger, R., A Koszul sign map, arXiv:1708.01430 (2017).Google Scholar
Bergman, G. M., A note on abelian categories – translating element-chasing proofs, and exact embedding in abelian groups, http://math.berkeley.edu/~gbergman/papers/unpub/elem-chase.pdf.Google Scholar
Bernstein, I. N., Gelfand, I. M. and Ponomarev, V. A., Coxeter functors and Gabriel’s theorem, Uspekhi Mat. Nauk 28 (1973), 1923, Trans.: Russian Math. Surveys 28 (1973), 17–32.Google Scholar
Bernstein, J. and Lunts, V., Equivariant Sheaves and Functors, Lecture Notes in Mathematics 1578, Springer, 1994.CrossRefGoogle Scholar
Berthelot, P., Grothendieck, A. and Illusie, L., eds., Séminaire de Géométrie Algébrique du Bois Marie – 1966-67 – Théorie des intersections et théorème de Riemann-Roch, SGA 6, Lecture Notes in Mathematics 225, Springer, 1971.Google Scholar
Björk, J.E., The Auslander condition on noetherian rings, in Séminaire Dubreil-Malliavin, 1987–1988, Lecture Notes in Mathematics 1404, Springer, 1989, pp. 137173.Google Scholar
Bokstedt, M. and Neeman, A., Homotopy limits in triangulated categories, Compositio Math. 86 (1993), 209234.Google Scholar
Bondal, A. I. and Kapranov, M. M., Representable functors, Serre functors, and mutations, Math. USSR Izvestia 35 (1990), 519541.Google Scholar
Bondal, A. I. and Kapranov, M. M., Enhanced triangulated categories, Math. USSR Sbornik, 70 (1991), 93107.Google Scholar
Bondal, A. and Van den Bergh, M., Generators and representability of functors in commutative and noncommutative geometry, Moscow Math. J. 3, Number 1 (2003), 136.Google Scholar
Borel, A., Algebraic D-Modules, Academic Press, 1987.Google Scholar
Bourbaki, N., Commutative Algebra, Hermann, Paris, 1972.Google Scholar
Brenner, S. and Butler, M. C. R., Generalizations of the Bernstein– Gelfand–Ponomarev reflection functors, in Proceedings ICRA II, Lecture Notes in Mathematics 832, Springer, 1980, pp. 103169.Google Scholar
Brodmann, M. P. and Sharp, R. Y., Local Cohomology: An Algebraic Introduction with Geometric Applications, Cambridge Studies in Advanced Mathematics 136, 2nd edition, Cambridge University Press, 2013.Google Scholar
Brown, E., Cohomology theories, Ann. Math. 75 (1962), 467484.Google Scholar
Brown, K. A. and Zhang, J. J., Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras, J. Algebra 320, No. 5 (2008), 18141850.Google Scholar
Buan, A. B., Marsh, R., Reineke, M., Reiten, I. and Todorov, G., Tilting theory and cluster combinatorics, Adv. Math. 204 (2006), 572618.Google Scholar
Buchweitz, R.-O., Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings (1986), 155 pp., http:hdl.handle.net/1807/16682.Google Scholar
Buchweitz, R.-O., Green, E. L., Madsen, D. and Solberg, O.. Finite Hochschild cohomology without finite global dimension, Math. Res. Lett. 12 (2005), 805816.CrossRefGoogle Scholar
Caldero, P., Chapoton, F. and Schiffler, R., Quivers with relations and cluster tilted algebras, Algebr. Represent. Theory 9 (2006), 359376.Google Scholar
Canonaco, A., Ornaghi, M. and Stellari, P., Localizations of the category of A categories and internal Homs, arXiv:1811.07830 (2018).Google Scholar
Canonaco, A. and Stellari, P., A tour about existence and uniqueness of dg enhancements and lifts, J. Geom. Phys. 122 (2017), 2852.Google Scholar
Chan, D., Wu, Q. S. and Zhang, J. J., Pre-balanced dualizing complexes, Israel J. Math. 132 (2002), 285314.Google Scholar
Chen, X.W., A note on standard equivalences, Bulletin LMS 48 (2016), 797801.Google Scholar
Cline, E., Parshall, B. and Scott, L., Derived categories and Morita theory, J. Algebra 104 (1986), 397409.Google Scholar
Costello, K. J., Topological conformal field theories and Calabi–Yau categories, Adv. Math. 210 (2007), 165214.Google Scholar
Craven, D. A. and Rouquier, R., Perverse equivalences and Broué’s conjecture, Adv. Math. 248 (2013), 158.Google Scholar
Dold, A. and Puppe, D., Homologie nicht-additiver Funktoren, Annales de l’Institut Fourier 11 (1961), 201312.Google Scholar
Dugger, D. and Shipley, B., Topological equivalences of differential graded algebras, Adv. Math. 212 (2007), 3761.Google Scholar
Eisenbud, D., Commutative Algebra, Springer, 1994.Google Scholar
Freyd, P., Abelian Categories, Harper, 1966.Google Scholar
Fukaya, K., Morse homotopy, A-category and Floer homologies, MSRI preprint No. 020-94, 1993.Google Scholar
Gabriel, P. and Zisman, M., Calculus of Fractions and Homotopy Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, 1967.Google Scholar
Gaitsgory, D., Recent progress in geometric Langlands theory, www.math.harvard.edu/~gaitsgde/GL/Bourb.pdf.Google Scholar
Gelfand, S. I. and Manin, Y. I., Methods of Homological Algebra, Springer, 2002.Google Scholar
Ginzburg, V., Calabi–Yau algebras, eprint arXiv:math/0612139 (2007).Google Scholar
Grothendieck, A., Sur quelques points d’algèbre homologique, Tôhoku Math. J. 9 (1957), 119221.Google Scholar
Grothendieck, A., Local Cohomology (Lecture Notes by R. Hartshorne), Lecture Notes in Mathematics 41, Springer, 1967.Google Scholar
Grothendieck, A. and Dieudonné, J., Éléments de géometrie algébrique, collective reference for the whole series.Google Scholar
Grothendieck, A. and Dieudonné, J., Éléments de géometrie algébrique, Chapitre III, Première partie, Publ. Math. IHES 11, 1961.Google Scholar
Grothendieck, A. and Dieudonné, J., Éléments de géometrie algébrique, Chapitre IV, Quatrième partie, Publ. Math. IHES 32, 1967.Google Scholar
Happel, D., On the derived category of a finite-dimensional algebra, Commentarii Mathematici Helvetici 62 (1987), 339389.Google Scholar
Happel, D., Triangulated Categories in the Representation of Finite Dimensional Algebras, Cambridge University Press, 1988.Google Scholar
Happel, D., Hochschild cohomology of finite-dimensional algebras, in Séminaire d’Algèbre Paul Dubreil et Marie-Paul Malliavin, Lecture Notes in Mathematics 1404, Springer, 1989, pp. 108126.Google Scholar
Happel, D. and Ringel, C. M., Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 399443.Google Scholar
Hartshorne, R., Residues and Duality, Lecture Notes in Mathematics 20, Springer, 1966.Google Scholar
Hartshorne, R., Algebraic Geometry, Springer, 1977.CrossRefGoogle Scholar
Hille, L. and Van den Bergh, M., Fourier-Mukai transforms, in Handbook of Tilting Theory, London Math. Soc. Lecture Note Ser. 332 (2006), pp. 147173.Google Scholar
Hilton, P. J. and Stammbach, U., A Course in Homological Algebra, Springer, 1971.Google Scholar
Hinich, V., Homological algebra of homotopy algebras, Comm. Algebra 25 (1997), 3291–3323. Erratum arXiv:math/0309453.Google Scholar
Hinich, V., Lectures on infinity categories, arXiv:1709.06271 (2018).Google Scholar
Hovey, M., Model categories, Math. Surv. Monogr. 63, AMS, 1999.Google Scholar
Huisgen-Zimmermann, B. and Saorin, M., Geometry of chain complexes and outer automorphism groups under derived equivalence, Trans. Amer. Math. Soc. 353 (2001), 47574777.CrossRefGoogle Scholar
Huybrechts, D., Fourier-Mukai Transforms in Algebraic Geometry, Oxford Mathematical Monographs, 2006.Google Scholar
Jacobson, N., Basic Algebra I, Freeman, 1974.Google Scholar
Jørgensen, P., Local cohomology for non-commutative graded algebras, Comm. Algebra 25 (1997), 575591.Google Scholar
Kadeisvili, T. V., On the theory of homology of fiber spaces, Uspekhi Mat. Nauk 35 (1980), 183188.Google Scholar
Kashiwara, M., D-Modules and Microlocal Calculus, AMS, 2003.Google Scholar
Kashiwara, M. and Schapira, P., Sheaves on Manifolds, Springer, 1990.Google Scholar
Kashiwara, M. and Schapira, P., Categories and Sheaves, Springer, 2005.Google Scholar
Kashiwara, M. and Schapira, P., DQ Modules, Astérisque 345, 2012.Google Scholar
Keller, B., Chain complexes and stable categories, Manus. Math. 67 (1990), 379417.Google Scholar
Keller, B., Deriving DG categories, Ann. Sci. Ecole Norm. Sup. 27 (1994) 63102.Google Scholar
Keller, B., Introduction to A-infinity algebras and modules, Homology Homotopy App., 3 (2001), 135. Addendum: Homology Homotopy Appl. 4 (2002), 25–28.Google Scholar
Keller, B., Hochschild cohomology and derived Picard groups, J. Pure Appl. Algebra 190 (2004), 177196.Google Scholar
Keller, B., On triangulated orbit categories, Doc. Math. 10 (2005), 551581.Google Scholar
Keller, B., A-infinity algebras, modules and functor categories, in Trends in Representation Theory of Algebras and Related Topics, Contemp. Math. 406, AMS, 2006, pp. 6793.Google Scholar
Keller, B., Cluster algebras and derived categories, in Derived Categories in Algebraic Geometry, EMS, 2013, pp. 123184.Google Scholar
Kelly, G. M., Chain maps inducing zero homology maps, Proc. Cambridge Philos. Soc. 61 (1965), 847854.Google Scholar
Kontsevich, M., Homological algebra of mirror symmetry, in Proceedings of the International Congress of Mathematicians, Zurich, Switzerland 1994, Vol. 1, Birkhauser, 1995, pp. 120139.Google Scholar
Kontsevich, M. and Soibelman, Y., Homological mirror symmetry and torus fibrations, in Symplectic Geometry and Mirror Symmetry, World Sci. Publishing, 2001, pp. 203–263.Google Scholar
Kontsevich, M. et al., Simons collaboration on homological mirror symmetry, https://schms.math.berkeley.edu.Google Scholar
Koszul, J. L., Sur un type d’algébres différentielles en rapport avec la transgression, in Colloque de topologie (espaces fibrés), Masson, 1951, pp. 7381.Google Scholar
Krause, H., Localization theory for triangulated Categories, in Triangulated Categories, London Math. Soc. Lecture Note Ser. 375, 2010, pp. 161253.Google Scholar
Kuznetsov, A., Calabi–Yau and fractional Calabi–Yau categories, J. Reine Angew. Math. 753 (2019), 239267.Google Scholar
Ladkani, S., 2-CY-tilted algebras that are not Jacobian, arXiv:1403.6814 (2014).Google Scholar
Lam, T.-Y., Lectures on Modules and Rings, Springer, 1999.Google Scholar
Lefèvre-Hasegawa, K., Sur les A-categories, Ph.D. thesis (2003), arXiv:0310337v1.Google Scholar
Levasseur, T., Some properties of noncommutative regular rings, Glasgow Math. J. 34 (1992), 277300.Google Scholar
Lipman, J., Nayak, S. and Sastry, P., Pseudofunctorial behavior of Cousin complexes on formal schemes, in Variance and Duality for Cousin Complexes on Formal Schemes, Contemp. Math. 375, AMS, 2005, pp. 3133.Google Scholar
Lipman, J., Dualizing Sheaves, Differentials and Residues on Algebraic Varieties, Astérisque 117, 1984.Google Scholar
Lipman, J., Notes on derived functors and Grothendieck duality, in Foundations of Grothendieck Duality for Diagrams of Schemes, Lecture Notes in Mathematics 1960, Springer, 2009.Google Scholar
Lurie, J., Books and papers on derived algebraic geometry, www.math.harvard.edu/~lurie.Google Scholar
Lurie, J., Higher algebra, www.math.harvard.edu/~lurie/papers/HA.pdf.Google Scholar
Maclane, S., Homology, Springer, 1994 (reprint).Google Scholar
Maclane, S., Categories for the Working Mathematician, Springer, 1978.Google Scholar
Macri, E. and Stellari, P., Lectures on non-commutative K3 surfaces, Bridgeland stability, and moduli spaces, arXiv:1807.06169 (2019).Google Scholar
Matlis, E., Injective modules over Noetherian rings, Pacific J. Math. 8, 3 (1958), 511528.Google Scholar
Matsumura, H., Commutative Ring Theory, Cambridge University Press, 1986.Google Scholar
McConnell, J. C. and Robson, J. C., Noncommutative Noetherian Rings, Wiley, 1987.Google Scholar
McConnell, J. C. and Stafford, J. T., Gelfand-Kirillov dimension and associated graded modules, J. Algebra 125 (1989), 197214.Google Scholar
Milne, J. S., Étale Cohomology, Princeton University Press, 1980.Google Scholar
Miyachi, J.-I. and Yekutieli, A., Derived Picard groups of finite dimensional hereditary algebras, Compositio Math. 129 (2001), 341368.Google Scholar
Nadler, D. and Zaslow, E., Constructible sheaves and the Fukaya category, J. Amer. Math. Soc. 22 (2009), 233286.Google Scholar
Nǎstǎsescu, C. and Van Oystaeyen, F., Graded and Filtered Rings and Modules, Lecture Notes in Mathematics 758, Springer, 1979.Google Scholar
Neeman, A., The connection between the K-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel, Ann. Sci. École Norm. Sup. 25 (1992), 547566.Google Scholar
Neeman, A., Triangulated Categories, Princeton University Press, 2001.Google Scholar
Neeman, A., The Grothendieck duality theorem via Bousfield’s techniques and Brown representability, J. AMS 9, (1996), 205236.Google Scholar
The nLab, an online source for mathematics etc., http://ncatlab.org.Google Scholar
Olsson, M., Algebraic Spaces and Stacks, AMS Colloquium Publications 62, 2016.Google Scholar
Orlov, D. O., Triangulated categories of singularities and D-branes in Landau-Ginzburg models, Tr. Mat. Inst. Steklova 246 (2004), 240262.Google Scholar
Porta, M., Shaul, L. and Yekutieli, A., On the homology of completion and torsion, Algebr. Repesent. Theory 17 (2014), 3167. Erratum: Algebr. Represent. Theory, 18 (2015), 1401–1405.Google Scholar
Porta, M., Shaul, L. and Yekutieli, A., Completion by derived double centralizer, Algebr. Represent. Theory 17 (2014), 481494.Google Scholar
Porta, M., Shaul, L. and Yekutieli, A., Cohomologically cofinite complexes, Comm. Algebra 43 (2015), 597615.Google Scholar
Positselski, L., Dedualizing complexes of bicomodules and MGM duality over coalgebras, Algebr. Represent. Theor. 21 (2018), 737767.Google Scholar
Quillen, D., Higher algebraic K-theory I, in Higher K-Theories, Lecture Notes in Mathematics 341, Springer, 1973, pp. 85147.CrossRefGoogle Scholar
Reyes, M., Rogalski, D. and Zhang, J. J., Skew Calabi–Yau triangulated categories and Frobenius Ext-algebras, Trans. Amer. Math. Soc. 369 (2017), 309340.Google Scholar
Reyes, M. and Rogalski, D., A twisted Calabi–Yau toolkit, eprint arXiv:1807.10249 (2018).Google Scholar
Rickard, J., Derived categories and stable equivalence, J. Pure Appl. Algebra 61 (1989), 303317.CrossRefGoogle Scholar
Rickard, J., Morita theory for derived categories, J. London Math. Soc. 39 (1989), 436456.Google Scholar
Rickard, J., Derived equivalences as derived functors, J. London Math. Soc. 43 (1991), 3748.Google Scholar
Rogalski, D., Idealizer rings and noncommutative projective geometry, J. Algebra 279 (2004), 791809.Google Scholar
Rotman, J., An Introduction to Homological Algebra, Academic Press, 1979.Google Scholar
Rowen, L. R., Ring Theory (Student Edition), Academic Press, 1991.Google Scholar
Rouquier, R., Automorphismes, graduations et catégories triangulées, J. Inst. Math. Jussieu, 10 (2011), 713751.CrossRefGoogle Scholar
Rouquier, R. and Zimmermann, A., Picard groups for derived module categories, Proc. London Math. Soc. 87 (2003), 197225.Google Scholar
Saorin, M., Dg algebras with enough idempotents, their dg modules and their derived categories, Algebra Discrete Math. 23 (2017), 62137.Google Scholar
Sato, M., Kawai, T. and Kashiwara, M., Microfunctions and pseudo-differential equations, in Hyperfunctions and Pseudo-Differential Equations, Lecture Notes in Mathematics 287, Springer, 1973, pp. 265529.Google Scholar
Schwede, S., Algebraic versus topological triangulated categories, in Proceedings of Conference on Triangulated Categories (Leeds 2006), London Math. Soc. Lecture Note Ser. 375 (2006).Google Scholar
Schwede, S. and Shipley, B., Stable model categories are categories of modules, Topology 42 (2003), 103153.Google Scholar
Shaul, L., Hochschild cohomology commutes with adic completion, Algebra Number Theory 10 (2016), 10011029.Google Scholar
Shaul, L., Reduction of Hochschild cohomology over algebras finite over their center, J. Pure Appl. Algebra 219 (2015), 43684377.Google Scholar
Shaul, L., Relations between derived Hochschild functors via twisting, Comm. Algebra 44 (2016), 28982907.Google Scholar
Shipley, B., Morita theory in stable homotopy theory, in Handbook of Tilting Theory, London Math. Soc. Lecture Note Ser. 332 (2006), 393409.Google Scholar
Seidel, P., Fukaya Categories and Picard–Lefschetz Theory, Zürich Lectures in Advanced Mathematics, EMS, Zürich, 2008.Google Scholar
Solotar, A. and Zadunaisky, P., Change of grading, injective dimension and dualizing complexes, Comm. Algebra 46 (2018), 44144425.Google Scholar
Spaltenstein, N., Resolutions of unbounded complexes, Compositio Math. 65 (1988), 121154.Google Scholar
The Stacks Project, an online reference, J. A. de Jong (ed.), http://stacks.math.columbia.edu.Google Scholar
Stafford, J. T. and Van den Bergh, M., Noncommutative curves and noncommutative surfaces, Bull. Amer. Math. Soc. 38 (2001), 171216.Google Scholar
Stasheff, J. D., Homotopy associativity of H-spaces, I, Trans. AMS 108 (1963), 275292.Google Scholar
Stasheff, J. D., Homotopy associativity of H-spaces, II, Trans. AMS 108 (1963), 293312.Google Scholar
Stenström, B., Rings of Quotients, Springer, 1975.Google Scholar
Tamarkin, D., Microlocal conditions for non-displaceability, arXiv:0809.1584 (2008).Google Scholar
Thomason, R. W. and Trobaugh, T., Higher algebraic K-theory of schemes and of derived categories, in The Grothendieck Festschrift, Progress in Mathematics 88, Birkhäuser, 1990, pp. 247435.Google Scholar
Toën, B., Lectures on DG-categories, in Topics in Algebraic and Topological K-Theory, Lecture Notes in Mathematics 2008, Springer, 2011.Google Scholar
Toën, B., Derived algebraic geometry, EMS Surv. Math. Sci. 1 (2014), 153240.Google Scholar
Van den Bergh, M., Existence theorems for dualizing complexes over non-commutative graded and filtered rings, J. Algebra 195 (1997), 662679.Google Scholar
Van den Bergh, M., A relation between Hochschild homology and cohomology for Gorenstein rings, Proc. Amer. Math. Soc. 126 (1998), 13451348. Erratum: Proc. Amer. Math. Soc. 130 (2002), 2809–2810.Google Scholar
Verdier, J.-L., Catégories Dérivées, état 0, Lecture Notes in Mathematics 569, Springer, 1977.Google Scholar
Verdier, J.-L., Des Catégories Dérivées des Catégories Abéliennes, Astérisque 239, 1996.Google Scholar
Vyas, R. and Yekutieli, A., Weak proregularity, weak stability, and the noncommutative MGM equivalence, J. Algebra 513 (2018), 265325.Google Scholar
Weibel, C., An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics 38, 1994.Google Scholar
Wu, Q. S. and Zhang, J. J., Some homological invariants of local PI algebras, J. Algebra 225 (2000), 904935.Google Scholar
Wu, Q.S. and Zhang, J. J., Dualizing complexes over noncommutative local rings, J. Algebra 239 (2001), 513548.Google Scholar
Yekutieli, A., Dualizing complexes over noncommutative graded algebras, J. Algebra 153 (1992), 4184.Google Scholar
Yekutieli, A., An Explicit Construction of the Grothendieck Residue Complex, Astérisque 208, 1992.Google Scholar
Yekutieli, A., The residue complex of a noncommutative graded algebra, J. Algebra 186 (1996), 522543.Google Scholar
Yekutieli, A., Residues and differential operators on schemes, Duke Math. J. 95 (1998), 305341.Google Scholar
Yekutieli, A., Dualizing complexes, Morita equivalence and the derived Picard group of a ring, with appendix by E. Kreines, J. London Math. Soc. 60 (1999), 723746.Google Scholar
Yekutieli, A., The rigid dualizing complex of a universal enveloping algebra, J. Pure Appl. Algebra 150 (2000), 8593.Google Scholar
Yekutieli, A., The derived Picard group is a locally algebraic group, Algebras Representation Theory 7 (2004), 5357.Google Scholar
Yekutieli, A., Rigid dualizing complexes via differential graded algebras (survey), in Proceedings of Conference on Triangulated Categories (Leeds 2006), London Math. Soc. Lecture Note Ser. 375 (2006).Google Scholar
Yekutieli, A., Continuous and twisted L morphisms, J. Pure Appl. Algebra 207 (2006), 575606.Google Scholar
Yekutieli, A., A Course on Derived Categories, arXiv:1206.6632v2, (2015).Google Scholar
Yekutieli, A., Central extensions of Gerbes, Adv. Math. 225 (2010), 445486.Google Scholar
Yekutieli, A., Duality and tilting for commutative DG rings, arXiv:1312.6411v4 (2016).Google Scholar
Yekutieli, A., The squaring operation for commutative DG rings, J. Algebra 449 (2016), 50107.Google Scholar
Yekutieli, A., Residues and duality for schemes and stacks, lecture notes (2013), www.math.bgu.ac.il/~amyekut/lectures/resid-stacks/handout.pdf.Google Scholar
Yekutieli, A., Rigidity, residues and duality for commutative rings, in preparation (2019).Google Scholar
Yekutieli, A., Rigidity, residues and duality for schemes, in preparation (2019).Google Scholar
Yekutieli, A., Rigidity, residues and duality for DM stacks, in preparation (2019).Google Scholar
Yekutieli, A., Derived categories of bimodules, in preparation (2019).Google Scholar
Yekutieli, A., The derived category of sheaves of commutative DG rings, lecture notes (2017), www.math.bgu.ac.il/~amyekut/lectures/shvs-dgrings/notes.pdf.Google Scholar
Yekutieli, A., Derived categories of bimodules, lecture notes (2016), www .math.bgu.ac.il/∼amyekut/lectures/der-cat-bimodules/abstract.html.Google Scholar
Yekutieli, A., Another proof of a theorem of Van den Bergh about graded-injective modules, arXiv:1407.5916 (2014).Google Scholar
Yekutieli, A. and Zhang, J. J., Serre duality for noncommutative projective schemes, Proc. Amer. Math. Soc. 125 (1997), 697707.Google Scholar
Yekutieli, A. and Zhang, J. J., Rings with Auslander dualizing complexes, J. Algebra 213 (1999), 151.Google Scholar
Yekutieli, A. and Zhang, J., Multiplicities of indecomposable injectives, J. London Math. Soc. 71 (2005), 100120.Google Scholar
Yekutieli, A. and Zhang, J., Homological transcendence degree, Proc. London Math. Soc. 93 (2006) 105137.Google Scholar
Yekutieli, A. and Zhang, J.J., Dualizing complexes and perverse modules over differential algebras, Compositio Math. 141 (2005), 620654.Google Scholar
Yekutieli, A. and Zhang, J., Dualizing complexes and perverse sheaves on noncommutative ringed schemes, Selecta Math. 12 (2006), 137177.Google Scholar
Yekutieli, A. and Zhang, J. J., Rigid complexes via DG algebras, Trans. AMS 360 (2008), 32113248.Google Scholar
Yekutieli, A. and Zhang, J. J., Rigid dualizing complexes over commutative rings, Algebras Representation Theory 12 (2009), 1952.Google Scholar
Yekutieli, A. and Zhang, J.J., Residue complexes over noncommutative rings, J. Algebra 259 (2003), 451493.Google Scholar

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  • References
  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book: Derived Categories
  • Online publication: 15 November 2019
  • Chapter DOI: https://doi.org/10.1017/9781108292825.020
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  • References
  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book: Derived Categories
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  • Chapter DOI: https://doi.org/10.1017/9781108292825.020
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  • References
  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book: Derived Categories
  • Online publication: 15 November 2019
  • Chapter DOI: https://doi.org/10.1017/9781108292825.020
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