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  • Print publication year: 2011
  • Online publication date: January 2012

Galois theory and Diophantine geometry

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[1] Beilinson, A.; Deligne, P.Interpretation motivique de la conjecture de Zagier reliant polylogarithmes et régulateurs. Motives (Seattle, WA, 1991), 97–121, Proc. Sympos. Pure Math., 55, Part 2, Amer. Math. Soc., Providence, RI, 1994.
[2] Bloch, Spencer; Kato, Kazuya. L-functions and Tamagawa numbers of motives. The Grothendieck Festschrift, Vol. I, 333–400, Progr. Math., 86, Birkhauser Boston, Boston, MA, 1990.
[3] Balakrishnan, Jennifer S.; Kedlaya, Kiran S.; Kim, Minhyong Appendix and erratum: ‘Massey products for elliptic curves of rank 1.’; Jour. Amer. Math. Soc. (to be published).
[4] Coates, John; Kim, Minhyong. Selmer varieties for curves with CM Jacobians. To be published, Kyoto Mathematical Journal. Available at the mathematics archive, arXiv:0810.3354.
[5] Coates, John; Fukaya, Takako; Kato, Kazuya; Sujatha, Ramdorai; Venjakob, Otmar. The GL2 main conjecture for elliptic curves without complex multiplication. Publ. Math. Inst. Hautes Études Sci. No. 101 (2005), 163–208.
[6] Coates, J.; Wiles, A.On the conjecture of Birch and Swinnerton-Dyer. Invent. Math. 39 (1977), no. 3, 223–251.
[7] Coleman, Robert F.Effective Chabauty. Duke Math. J. 52 (1985), no. 3, 765–770.
[8] Deligne, Pierre. Le groupe fondamental de la droite projective moins trois points. Galois groups over ℚ (Berkeley, CA, 1987), 79–297, Math. Sci. Res. Inst. Publ., 16, Springer, New York, 1989.
[9] Faltings, G.Endlichkeitssätze für abelsche Varietäten über Zahlkörpern. Invent. Math. 73 (1983), no. 3, 349–366.
[10] Fontaine, Jean-Marc. Sur certains types de représentations p-adiques du groupe de Galois d'un corps local; construction d'un anneau de Barsotti-Tate. Ann. of Math. (2) 115 (1982), no. 3, 529–577.
[11] Fontaine, Jean-Marc; Mazur, Barry. Geometric Galois representations. Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993), 41–78, Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995.
[12] Furusho, Hidekazu. p-adic multiple zeta values. I. p-adic multiple polylogarithms and the p-adic KZ equation. Invent. Math. 155 (2004), no. 2, 253–286.
[13] Goldman, William M.; Millson, John J.The deformation theory of representations of fundamental groups of compact Kähler manifolds. Inst. Hautes Études Sci. Publ. Math. No. 67 (1988), 43–96.
[14] Greenberg, Ralph. The Iwasawa invariants of Γ-extensions of a fixed number field. Amer. J. Math. 95 (1973), 204–214.
[15] Greenberg, Ralph. On the structure of certain Galois groups. Invent. Math. 47 (1978), no. 1, 85–99.
[16] Grothendieck, Alexander. Brief, an G., Faltings. London Math. Soc. Lecture Note Ser., 242, Geometric Galois actions, 1, 49–58, Cambridge University Press, Cambridge, 1997.
[17] Hain, Richard M.The de Rham homotopy theory of complex algebraic varieties. I. K-Theory 1 (1987), no. 3, 271–324.
[18] Iyanaga, Shokichi. Memories of Professor Teiji Takagi [1875–1960]. Class field theory–its centenary and prospect (Tokyo, 1998), 1–11, Adv. Stud. Pure Math., 30, Math. Soc. Japan, Tokyo, 2001.
[19] Motives. Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington, Seattle, Washington, July 20–August 2, 1991. Edited by Uwe Jannsen, Steven Kleiman and Jean-Pierre Serre. Proceedings of Symposia in Pure Mathematics, 55, Part 1. American Mathematical Society, Providence, RI, 1994. xiv+747 pp. ISBN: 0-8218-1636-5
[20] Kato, Kazuya. p-adic Hodge theory and values of zeta functions of modular forms. Cohomologies p-adiques et applications arithmétiques. III. Astérisque No. 295 (2004), ix, 117–290.
[21] Kato, Kazuya. Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions via BdR. I. Arithmetic algebraic geometry (Trento, 1991), 50–163, Lecture Notes in Math., 1553, Springer, Berlin, 1993.
[22] Kim, Minhyong. The motivic fundamental group of ℙ1 \{0, 1, ∞} and the theorem of Siegel. Invent. Math. 161 (2005), no. 3, 629–656.
[23] Kim, Minhyong. The unipotent Albanese map and Selmer varieties for curves. Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, 89–133. (Proceedings of special semester on arithmetic geometry, Fall, 2006.)
[24] Kim, Minhyong. Remark on fundamental groups and effective Diophantine methods for hyperbolic curves. To be published in Serge Lang memorial volume. Available at mathematics archive, arXiv:0708.1115.
[25] Kim, Minhyong. p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplication. Annals of Mathematics, 172 (2010), no. 1, 751–759.
[26] Kim, Minhyong. Massey products for elliptic curves of rank 1. Jour. Amer. Math. Soc. 23 (2010), no. 3, 725–748.
[27] Kim, Minhyong, and Tamagawa, Akio. The l-component of the unipotent Albanese map. Math. Ann. 340 (2008), no. 1, 223–235.
[28] Kolyvagin, Victor A.On the Mordell–Weil group and the Shafarevich–Tate group of modular elliptic curves. Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), 429–436, Math. Soc.Japan, Tokyo, 1991.
[29] Mumford, David; Fogarty, John. Geometric invariant theory. Second edition. Ergebnisse der Mathematik und ihrer Grenzgebiete, 34. Springer-Verlag, Berlin, 1982. xii+220 pp.
[30] Milne, J. S.Arithmetic duality theorems. Perspectives in Mathematics, 1. Academic Press, Inc., Boston, MA, 1986.
[31] Nakamura, Hiroaki; Tamagawa, Akio; Mochizuki, Shinichi. The Grothendieck conjecture on the fundamental groups of algebraic curves [translation of Su-gaku 50 (1998), no. 2, 113–129; MR1648427 (2000e:14038)]. Sugaku Expositions. Sugaku Expositions 14 (2001), no. 1, 31–53.
[32] Narasimhan, M. S.; Seshadri, C. S.Stable and unitary vector bundles on a compact Riemann surface. Ann. of Math. (2) 82 1965 540–567.
[33] Olsson, Martin. The bar construction and affine stacks. Preprint. Available at http://math.berkeley.edu/molsson/.
[34] Poonen, Bjorn. Computing rational points on curves. Number theory for the millennium, III (Urbana, IL, 2000), 149–172, A K Peters, Natick, MA, 2002.
[35] Reutenauer, Christophe. Free Lie algebras. London Mathematical Society Monographs. New Series, 7. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993.
[36] Rubin, Karl. The “main conjectures” of Iwasawa theory for imaginary quadratic fields. Invent. Math. 103 (1991), no. 1, 25–68.
[37] Serre, Jean-Pierre. Galois cohomology. Translated from the French by Patrick Ion and revised by the author. Springer-Verlag, Berlin, 1997. x+210 pp.
[38] Serre, Jean-Pierre. Andr Weil 6 May 1906-6 August 1998 Biographical Memoirs of Fellows of the Royal Society, Vol. 45, (Nov., 1999), pp. 521–529
[39] Serre, Jean-Pierre. Lie algebras and Lie groups. 1964 lectures given at Harvard University. Second edition. Lecture Notes in Mathematics, 1500. Springer-Verlag, Berlin, 1992. viii+168 pp.
[40] Simpson, Carlos T.Higgs bundles and local systems. Inst. Hautes Études Sci. Publ. Math. No. 75 (1992), 5–95.
[41] Szamuely, Tamas. Galois Groups and Fundamental Groups. Cambridge Studies in Advanced Mathematics, vol. 117, Cambridge University Press, 2009.
[42] Venjakob, Otmar. On the Iwasawa theory of p-adic Lie extensions. Compositio Math. 138 (2003), no. 1, 1–54.
[43] Weil, André. L'arithmétique sur les courbes algébriques. Acta Math. 52 (1929), no. 1, 281–315.
[44] Weil, André. Généralisation des fonctions abéliennes. J. Math Pur. Appl. 17 (1938), no. 9, 47–87.
[45] Wiles, Andrew. Modular elliptic curves and Fermat's last theorem. Ann. of Math. (2) 141 (1995), no. 3, 443–551.