Cornut, Christophe; Peche Irissarry, Macarena
Harder–Narasimhan Filtrations for Breuil–Kisin–Fargues modules
Annales Henri Lebesgue, Volume 2 (2019), p. 415-480

Metadata

KeywordsIntegral p-adic Hodge theory, Harder–Narasimhan filtrations, Breuil–Kisin–Fargues modules

Abstract

We define and study Harder–Narasimhan filtrations on Breuil–Kisin–Fargues modules and related objects relevant to p-adic Hodge theory.


References

[And09] André, Yves Slope filtrations, Confluentes Math., Volume 1 (2009) no. 1, pp. 1-85 | Article

[BMS16] Bhatt, Bhargav; Morrow, Matthew; Scholze, Peter Integral p-adic Hodge theory (2016) https://arxiv.org/abs/1602.03148 (preprint)

[Bou64] Bourbaki, Nicolas Éléments de mathématique. Fasc. XXX. Algèbre commutative. Chapitre 5: Entiers. Chapitre 6: Valuations, Hermann, Actualités Scientifiques et Industrielles, Volume 1308 (1964), 207 pages | MR 0194450 | Zbl 0205.34302

[BvdB03] Bondal, Alexey; van den Bergh, Michel Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J., Volume 3 (2003) no. 1, pp. 1-36 | MR 1996800 | Zbl 1135.18302

[CN16] Cornut, Christophe; Nicole, Marc-Hubert Cristaux et immeubles, Bull. Soc. Math. Fr., Volume 144 (2016) no. 1, pp. 125-143 | MR 3481264 | Zbl 1387.20023

[Cor] Cornut, Christophe Filtrations and buildings http://webusers.imj-prg.fr/~christophe.cornut/papers.html (to appear in Mem. Am. Math. Soc.)

[Cor18] Cornut, Christophe On Harder–Narasimhan filtrations and their compatibility with tensor products, Confluentes Math., Volume 10 (2018) no. 2, pp. 3-49 | Article | MR MR3928223

[Cor19] Cornut, Christophe Mazur’s Inequality and Laffaille’s theorem, Math. Ann., Volume 374 (2019) no. 3-4, pp. 1657-1679 | MR MR3985120 | Zbl 07087162

[Dem86] Demazure, Michel Lectures on p-divisible groups, Springer, Lecture Notes in Mathematics, Volume 302 (1986), vi+98 pages (Reprint of the 1972 original) | MR MR883960 | Zbl 0247.14040

[DOR10] Dat, Jean-François; Orlik, Sascha; Rapoport, Michael Period domains over finite and p-adic fields, Cambridge University Press, Cambridge Tracts in Mathematics, Volume 183 (2010), xxii+372 pages | MR 2676072 | Zbl 1206.14001

[Far10] Fargues, Laurent La filtration de Harder–Narasimhan des schémas en groupes finis et plats, J. Reine Angew. Math., Volume 645 (2010), pp. 1-39 | Article | MR 2673421 | Zbl 1199.14015

[Far15] Fargues, Laurent Quelques résultats et conjectures concernant la courbe, De la géométrie algébrique aux formes automorphes (I), Société Mathématique de France (Astérisque) (2015) no. 369, pp. 325-374 | MR 3379639 | Zbl 1326.14109

[Far16] Fargues, Laurent Geometrization of the local Langlands correspondence: an overview (2016) https://arxiv.org/abs/1602.00999 (preprint)

[Far19] Fargues, Laurent Théorie de la réduction pour les groupes p-divisibles (2019) https://arxiv.org/abs/1901.08270 (preprint)

[FF18] Fargues, Laurent; Fontaine, Jean-Marc Courbes et fibrés vectoriels en théorie de Hodge p-adique, Société Mathématique de France, Astérisque (2018) | MR MR3917141 | Zbl 07005651

[Fon90] Fontaine, Jean-Marc Représentations p-adiques des corps locaux. I, The Grothendieck Festschrift, Vol. II, Birkhäuser (Progress in Mathematics) Volume 87 (1990), pp. 249-309 | MR 1106901 | Zbl 0743.11066

[GR03] Gabber, Ofer; Ramero, Lorenzo Almost ring theory, Springer, Lecture Notes in Mathematics, Volume 1800 (2003), vi+307 pages | Article | MR 2004652

[Gro05] Grothendieck, Alexander Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2), Société Mathématique de France, Documents Mathématiques, Volume 4 (2005), x+208 pages (Séminaire de Géométrie Algébrique du Bois Marie, 1962, Augmenté d’un exposé de Michèle Raynaud) | MR 2171939 | Zbl 1079.14001

[HM07] Hamilton, Tracy Dawn; Marley, Thomas Non-Noetherian Cohen–Macaulay rings, J. Algebra, Volume 307 (2007) no. 1, pp. 343-360 | Article | MR 2278059

[Iri16] Irissarry, Macarena Peche The reduction of G-ordinary crystalline representations with G-structures (2016) https://arxiv.org/abs/1611.08529 (preprint)

[Kap49] Kaplansky, Irving Elementary divisors and modules, Trans. Am. Math. Soc., Volume 66 (1949), pp. 464-491 | Article | MR 0031470

[Ked05] Kedlaya, Kiran S. Slope filtrations revisited, Doc. Math., Volume 10 (2005), pp. 447-525 | MR 2184462

[Ked16a] Kedlaya, Kiran S. Noetherian properties of Fargues–Fontaine curves, Int. Math. Res. Not. (2016) no. 8, pp. 2544-2567 | Article | MR 3519123

[Ked16b] Kedlaya, Kiran S. Some ring-theoretic properties of A inf (2016) https://arxiv.org/abs/1602.09016 (preprint)

[KL15] Kedlaya, Kiran S.; Liu, Ruochuan Relative p-adic Hodge theory: foundations, Société Mathématique de France, Astérisque, Volume 371 (2015) | MR 3379653 | Zbl 1370.14025

[Kot85] Kottwitz, Robert E. Isocrystals with additional structure, Compos. Math., Volume 56 (1985) no. 2, pp. 201-220 | MR 809866 | Zbl 0597.20038

[LWE16] Levin, Brandon; Wang-Erickson, Carl A Harder–Narasimhan theory for Kisin modules (2016) https://arxiv.org/abs/1606.00914 (preprint)

[Man63] Manin, Yuri I. Theory of commutative formal groups over fields of finite characteristic, Usp. Mat. Nauk, Volume 18 (1963) no. 6(114), pp. 3-90 | MR 0157972 | Zbl 0128.15603

[Nor76] Northcott, D. G. Finite free resolutions, Cambridge University Press, Cambridge Tracts in Mathematics, Volume 71 (1976), xii+271 pages | MR 0460383 | Zbl 0328.13010

[Sch17] Scholze, Peter p-adic Geometry (2017) https://arxiv.org/abs/1712.03708 (preprint)

[SW17] Scholze, Peter; Weinstein, Jared Peter Scholze’s lectures on p-adic geometry, Notes by J. Weinstein (2017) https://www.math.uni-bonn.de/people/scholze/Berkeley.pdf (to appear in Annals of Mathematics Studies)

[Zin84] Zink, Thomas Cartiertheorie kommutativer formaler Gruppen, Teubner Verlagsgesellschaft, Teubner-Texte zur Mathematik, Volume 68 (1984), 124 pages | MR 767090 | Zbl 0578.14039