Metadata
Abstract
We define and study Harder–Narasimhan filtrations on Breuil–Kisin–Fargues modules and related objects relevant to -adic Hodge theory.
References
[And09] Slope filtrations, Confluentes Math., Volume 1 (2009) no. 1, pp. 1-85 | Article | MR 2571693 | Zbl 1213.14039
[BMS16] Integral p-adic Hodge theory (2016) https://arxiv.org/abs/1602.03148 (preprint) | Zbl 07018374
[Bou64] Éléments de mathématique. Fasc. XXX. Algèbre commutative. Chapitre 5: Entiers. Chapitre 6: Valuations, Actualités Scientifiques et Industrielles, 1308, Hermann, 1964, 207 pages | MR 0194450 | Zbl 0205.34302
[BvdB03] Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J., Volume 3 (2003) no. 1, pp. 1-36 | Article | MR 1996800 | Zbl 1135.18302
[CN16] Cristaux et immeubles, Bull. Soc. Math. Fr., Volume 144 (2016) no. 1, pp. 125-143 | Article | MR 3481264 | Zbl 1387.20023
[Cor] Filtrations and buildings http://webusers.imj-prg.fr/~christophe.cornut/papers.html (to appear in Mem. Am. Math. Soc.)
[Cor18] On Harder–Narasimhan filtrations and their compatibility with tensor products, Confluentes Math., Volume 10 (2018) no. 2, pp. 3-49 | Article | MR MR3928223
[Cor19] Mazur’s Inequality and Laffaille’s theorem, Math. Ann., Volume 374 (2019) no. 3-4, pp. 1657-1679 | Article | MR MR3985120 | Zbl 07087162
[Dem86] Lectures on -divisible groups, Lecture Notes in Mathematics, 302, Springer, 1986, vi+98 pages (Reprint of the 1972 original) | MR MR883960 | Zbl 0247.14040
[DOR10] Period domains over finite and -adic fields, Cambridge Tracts in Mathematics, 183, Cambridge University Press, 2010, xxii+372 pages | MR 2676072 | Zbl 1206.14001
[Far10] 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] Quelques résultats et conjectures concernant la courbe, De la géométrie algébrique aux formes automorphes (I) (Astérisque), Société Mathématique de France, 2015 no. 369, pp. 325-374 | MR 3379639 | Zbl 1326.14109
[Far16] Geometrization of the local Langlands correspondence: an overview (2016) https://arxiv.org/abs/1602.00999 (preprint)
[Far19] Théorie de la réduction pour les groupes p-divisibles (2019) https://arxiv.org/abs/1901.08270 (preprint)
[FF18] Courbes et fibrés vectoriels en théorie de Hodge -adique, Astérisque, Société Mathématique de France, 2018 | MR MR3917141 | Zbl 07005651
[Fon90] Représentations -adiques des corps locaux. I, The Grothendieck Festschrift, Vol. II (Progress in Mathematics), Volume 87, Birkhäuser, 1990, pp. 249-309 | MR 1106901 | Zbl 0743.11066
[GR03] Almost ring theory, Lecture Notes in Mathematics, 1800, Springer, 2003, vi+307 pages | Article | MR 2004652 | Zbl 1045.13002
[Gro05] Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2), Documents Mathématiques, 4, Société Mathématique de France, 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] Non-Noetherian Cohen–Macaulay rings, J. Algebra, Volume 307 (2007) no. 1, pp. 343-360 | Article | MR 2278059 | Zbl 1109.13020
[Iri16] The reduction of -ordinary crystalline representations with -structures (2016) https://arxiv.org/abs/1611.08529 (preprint)
[Kap49] Elementary divisors and modules, Trans. Am. Math. Soc., Volume 66 (1949), pp. 464-491 | Article | MR 0031470 | Zbl 0036.01903
[Ked05] Slope filtrations revisited, Doc. Math., Volume 10 (2005), pp. 447-525 | MR 2184462 | Zbl 1081.14028
[Ked16a] Noetherian properties of Fargues–Fontaine curves, Int. Math. Res. Not. (2016) no. 8, pp. 2544-2567 | Article | MR 3519123 | Zbl 1404.13026
[Ked16b] Some ring-theoretic properties of (2016) https://arxiv.org/abs/1602.09016 (preprint)
[KL15] Relative -adic Hodge theory: foundations, Astérisque, 371, Société Mathématique de France, 2015 | MR 3379653 | Zbl 1370.14025
[Kot85] Isocrystals with additional structure, Compos. Math., Volume 56 (1985) no. 2, pp. 201-220 | Numdam | MR 809866 | Zbl 0597.20038
[LWE16] A Harder–Narasimhan theory for Kisin modules (2016) https://arxiv.org/abs/1606.00914 (preprint)
[Man63] 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] Finite free resolutions, Cambridge Tracts in Mathematics, 71, Cambridge University Press, 1976, xii+271 pages | MR 0460383 | Zbl 0328.13010
[Sch17] -adic Geometry (2017) https://arxiv.org/abs/1712.03708 (preprint)
[SW17] Peter Scholze’s lectures on -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] Cartiertheorie kommutativer formaler Gruppen, Teubner-Texte zur Mathematik, 68, Teubner Verlagsgesellschaft, 1984, 124 pages | MR 767090 | Zbl 0578.14039