Hostname: page-component-6bf8c574d5-t27h7 Total loading time: 0 Render date: 2025-02-27T15:08:08.075Z Has data issue: false hasContentIssue false
  • English
  • Français

Almost direct summands

Published online by Cambridge University Press:  11 January 2016

Bhargav Bhatt
Bhargav Bhatt*
Affiliation:
School of Mathematics Institute for Advanced Study Princeton, New Jersey 08540USAbhargav.bhatt@gmail.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove new cases of the direct summand conjecture using fundamental theorems in p-adic Hodge theory due to Faltings. The cases tackled include the ones when the ramification locus lies entirely in characteristic p.

Keywords

13H0513D2214B05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 214 , June 2014 , pp. 195 - 204
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

References

[F1] Faltings, G., p-adic Hodge theory, J. Amer. Math. Soc. 1 1988, 255–299. MR 0924705. DOI 10.2307/1990970.CrossRefGoogle Scholar
[F2] Faltings, G., “Almost étale extensions” in Cohomologies p-adiques et applications arithmétiques, II, Astérisque 279, Soc. Math. France, Paris, 2002, 185–270. MR 1922831.Google Scholar
[GR1] Gabber, O. and Ramero, L., Almost Ring Theory, Lecture Notes in Math. 1800, Springer, Berlin, 2003. MR 2004652.Google Scholar
[GR2] Gabber, O. and Ramero, L., Foundations of almost ring theory, preprint, arXiv:math/0409584v8[math.AG].Google Scholar
[Gro] Grothendieck, A., Revêtements étales et groupe fondamental, Séminaire de Géométrie Algébrique du Bois-Marie (SGA 1), Doc. Math. (Paris) 3, Soc. Math. France, Paris, 2003. MR 2017446.Google Scholar
[H] Heitmann, R. C., The direct summand conjecture in dimension three, Ann. of Math. (2) 156 2002, 695–712. MR 1933722. DOI 10.2307/3597204.CrossRefGoogle Scholar
[Ho1] Hochster, M., Contracted ideals from integral extensions of regular rings, Nagoya Math. J. 51 1973, 25–43. MR 0349656.CrossRefGoogle Scholar
[Ho2] Hochster, M., Canonical elements in local cohomology modules and the direct summand conjecture, J. Algebra 84 1983, 503–553. MR 0723406. DOI 10.1016/0021-8693(83)90092–3.CrossRefGoogle Scholar
[Ho3] Hochster, M., Homological conjectures, old and new, Illinois J. Math. 51 2007, 151–169. MR 2346192.CrossRefGoogle Scholar
[O] Olsson, M. C., “On Faltings’ method of almost étale extensions” in Algebraic Geometry (Seattle, 2005), Part 2, Proc. Sympos. Pure Math. 80 Part 2, Amer. Math. Soc., Providence, 2009, 811–936. MR 2483956.CrossRefGoogle Scholar
[R] Roberts, P., Almost regular sequences and the monomial conjecture, MichiganMath. J. 57 2008, 615–623. MR 2492472. DOI 10.1307/mmj/1220879428.CrossRefGoogle Scholar
[S] Scholze, P., Perfectoid spaces, Publ. Math. Inst. Hautes Etudes Sci. 116 2012, 245–313. MR 3090258. DOI 10.1007/s10240–012-0042-x.CrossRefGoogle Scholar
[T] Tate, J. T., “p-divisible groups” in Proceedings of a Conference on Local Fields (Driebergen, 1966), Springer, Berlin, 1967, 158–183. MR 0231827.CrossRefGoogle Scholar