Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-05-03T05:27:59.136Z Has data issue: false hasContentIssue false

5 - Abélianisation des espaces homogènes et applications arithmétiques

from PART TWO - CONTRIBUTED PAPERS

Published online by Cambridge University Press:  05 May 2013

C. Demarche
Affiliation:
Université Pierre et Marie Curie
Alexei N. Skorobogatov
Affiliation:
Imperial College London
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[Ald08] E., Aldrovandi – «2-gerbes bound by complexes of gr-stacks, and cohomology», J. Pure Appl. Algebra 212 (2008), no. 5, p. 994–1038.Google Scholar
[AN09] E., Aldrovandi et B., Noohi – «Butterflies. I. Morphisms of 2-group stacks», Adv. Math. 221 (2009), no. 3, p. 687–773.Google Scholar
[AN10] E., Aldrovandi et B., Noohi, «Butterflies II: torsors for 2-group stacks», Adv. Math. 225 (2010), no. 2, p. 922–976.Google Scholar
[Ana73] S., Anantharaman – «Schémas en groupes, espaces homogènes et espaces algébriques sur une base de dimension 1», Sur les groupes al-gébriques, Soc. Math. France, Paris, 1973, p. 5–79. Bull. Soc. Math. France, Mém. 33.Google Scholar
[BCTS08] M., Borovoi, J.-L., Colliot-Thélène et A. N., Skorobogatov – «The elementary obstruction and homogeneous spaces», Duke Math. J. 141 (2008), no. 2, p. 321–364.Google Scholar
[BD11] M., Borovoi et C., Demarche – «Manin obstruction to strong approximation for homogeneous spaces», Comment. Math. Helv. (2011), à paraître.Google Scholar
[Bor93] M., Borovoi – «Abelianization of the second nonabelian Galois co-homology», Duke Math. J. 72 (1993), no. 1, p. 217–239.Google Scholar
[Bor98] M., Borovoi, «Abelian Galois cohomology of reductive groups», Mem. Amer. Math. Soc. 132 (1998), no. 626, p. viii+50.Google Scholar
[Bor99] M., Borovoi, «The defect of weak approximation for homogeneous spaces», Ann. Fac. Sci. Toulouse Math. (6) 8 (1999), no. 2, p. 219–233.Google Scholar
[Bre90] L., Breen – «Bitorseurs et cohomologie non abélienne», The Grothendieck Festschrift, Vol. I, Progr. Math., vol. 86, Birkhäuser Boston, Boston, MA, 1990, p. 401–476.
[Bre92] L., Breen, «Théorie de Schreier supérieure», Ann. Sci. École Norm. Sup. (4) 25 (1992), no. 5, p. 465–514.Google Scholar
[Bre94] L., Breen, «On the classification of 2-gerbes and 2-stacks», Astérisque (1994), no. 225, p. 160.Google Scholar
[BvH11] M., Borovoi et J., van Hamel – «Extended equivariant Picard complexes and homogeneous spaces», Transform. Groups 17 (2012), p. 51–86.Google Scholar
[Con84] D., Conduché – «Modules croisés généralisés de longueur 2», J. Pure Appl. Algebra 34 (1984), no. 2-3, p. 155–178.Google Scholar
[CT08] J.-L., Colliot-Thélène – «Résolutions flasques des groupes linéaires connexes», J. Reine Angew. Math. 618 (2008), p. 77–133.Google Scholar
[CTGP04] J.-L., Colliot-Thélène, P., Gille et R., Parimala – «Arithmetic of linear algebraic groups over 2-dimensional geometric fields», Duke Math. J. 121 (2004), no. 2, p. 285–341.Google Scholar
[CTS87] J.-L., Colliot-Thélène et J.-J., Sansuc – «Principal homogeneous spaces under flasque tori: applications», J. Algebra 106 (1987), no. 1, p. 148–205.Google Scholar
[CTX09] J.-L., Colliot-Thélène et F., Xu – «Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms», Compos. Math. 145 (2009), no. 2, p. 309–363, With an appendix by Dasheng Wei and Fei Xu.Google Scholar
[Del79] P., Deligne – «Variétés de Shimura: interprétation modulaire, et techniques de construction de modèles canoniques», Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, p. 247–289.
[Dem09] C., Demarche – «Méthodes cohomologiques pour rationnels sur les espaces homogènes», Thèse de l'université Paris-Sud, 2009.
[Dem11a] C., Demarche, «Le défaut d'approximation connexes», Proc. Lond. Math. Soc. (3) 102 (2011), no. 3, p. 563–597.Google Scholar
[Dem11b] C., Demarche, «Suites de Poitou-Tate pour les complexes de tores á deux termes», Int. Math. Res. Not. IMRN (2011), no. 1, p. 135–174.Google Scholar
[Dem11c] C., Demarche, «Une formule pour le groupe de Brauer algébrique d'un torseur», J. Algebra 347 (2011), p. 96–132.Google Scholar
[GA11] C., Gonzalez-Aviles – «Quasi-abelian crossed modules and non-abelian cohomology», prépublication, 2011.Google Scholar
[Gir71] J., GiraudCohomologie non abélienne, Springer-Verlag, Berlin, 1971, Die Grundlehren der mathematischen Wissenschaften, Band 179.
[GP08] P., Gille et A., Pianzola – «Isotriviality and étale cohomology of Laurent polynomial rings», J. Pure Appl. Algebra 212 (2008), no. 4, p. 780–800.Google Scholar
[Gro66] A., Grothendieck – «Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. III», Inst. Hautes Études Sci. Publ. Math. (1966), no. 28, p. 255.Google Scholar
[Har67] G., Harder – «Halbeinfache Gruppenschemata über Dedekindringen», Inventiones Mathematicae 4 (1967), p. 165–191.Google Scholar
[Har08] D., Harari – «Le défaut d'approximation forte pour les groupes algébriques commutatifs», Algebra and Number Theory 2 (2008), no. 5, p. 595–611.Google Scholar
[HS05] D., Harari et T., Szamuely – «Arithmetic duality theorems for 1-motives», J. reine angew. Math. 578 (2005), p. 93–128, et Corrigenda for “Aritmetic duality theorems for 1-motives”, disponible sur http://www.math.u-psud/~harari/errata/corrigcrelle.pdf.Google Scholar
[HS08] D., Harari, «Local-global principles for 1-motives», Duke Math. J. 143 (2008), no. 3, p. 531–557.Google Scholar
[HS11] D., Harari et A., Skorobogatov – «Descent theory for open varieties», this volume.
[Jos09] P., Jossen – «The arithmetic of 1-motives», Thèse, 2009.
[Lab99] J.-P., Labesse – «Cohomologie, stabilisation et changement de base», Astérisque (1999), no. 257, p. vi+161, Appendix A by Laurent Clozel and Labesse, and Appendix B by Lawrence Breen.Google Scholar
[Mar91] G. A., MargulisDiscrete subgroups of semisimple Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 17, Springer-Verlag, Berlin, 1991.
[Mil80] J. S., MilneÉtale cohomology, Princeton Mathematical Series, vol. 33, Princeton University Press, Princeton, N.J., 1980.
[Mil06] J. S., Milne, Arithmetic duality theorems, second éd., BookSurge, LLC, Charleston, SC, 2006.
[Nis84] Y. A., Nisnevich – «Espaces homogènes principaux rationnellement triviaux et arithmétique des schémas en groupes réductifs sur les anneaux de Dedekind», C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 1, p. 5–8.Google Scholar
[NSW08] J., Neukirch, A., Schmidt et K., WingbergCohomology of number fields, second éd., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 323, Springer-Verlag, Berlin, 2008.
[PR94] V., Platonov et A., RapinchukAlgebraic groups and number theory, Pure and Applied Mathematics, vol. 139, Academic Press Inc., Boston, MA, 1994, Translated from the 1991 Russian original by Rachel Rowen.
[Ray70] M., RaynaudFaisceaux amples sur les schémas en groupes et les espaces homogènes, Lecture Notes in Mathematics, Vol. 119, Springer-Verlag, Berlin, 1970.
[Ros56] M., Rosenlicht – «Some basic theorems on algebraic groups», Amer. J. Math. 78 (1956), p. 401–443.Google Scholar
[San81] J.-J., Sansuc – «Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres», J. reine angew. Math. 327 (1981), p. 12–80.Google Scholar
[SGA3] M., Demazure et A., GrothendieckSchémas en groupes, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3). Dirigé par M. Demazure et A. Grothendieck. Lecture Notes in Mathematics, Vol. 151-152-153, Springer-Verlag, Berlin, 1970.

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×