Relevant bibliographies by topics / Breuil-Kisin module

Academic literature on the topic 'Breuil-Kisin module'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Breuil-Kisin module"

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Cais, Bryden, and Tong Liu. "Breuil–Kisin modules via crystalline cohomology." Transactions of the American Mathematical Society 371, no. 2 (September 20, 2018): 1199–230. http://dx.doi.org/10.1090/tran/7280.

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Hattori, Shin. "Canonical subgroups via Breuil–Kisin modules." Mathematische Zeitschrift 274, no. 3-4 (November 16, 2012): 933–53. http://dx.doi.org/10.1007/s00209-012-1102-0.

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Genestier, Alain, and Vincent Lafforgue. "Structures de Hodge–Pink pour les φ/𝔖-modules de Breuil et Kisin." Compositio Mathematica 148, no. 3 (May 2012): 751–89. http://dx.doi.org/10.1112/s0010437x11007238.

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AbstractIn this article, we apply the methods of our work on Fontaine’s theory in equal characteristics to the φ/𝔖-modules of Breuil and Kisin. Thanks to a previous article of Kisin, this yields a new and rather elementary proof of the theorem ‘weakly admissible implies admissible’ of Colmez and Fontaine.
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Hattori, Shin. "Canonical subgroups via Breuil–Kisin modules forp=2." Journal of Number Theory 137 (April 2014): 142–59. http://dx.doi.org/10.1016/j.jnt.2013.11.004.

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Cornut, Christophe, and Macarena Peche Irissarry. "Harder–Narasimhan Filtrations for Breuil–Kisin–Fargues modules." Annales Henri Lebesgue 2 (2019): 415–80. http://dx.doi.org/10.5802/ahl.22.

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Caruso, Xavier, Agnès David, and Ariane Mézard. "VARIÉTÉS DE KISIN STRATIFIÉES ET DÉFORMATIONS POTENTIELLEMENT BARSOTTI-TATE." Journal of the Institute of Mathematics of Jussieu 17, no. 5 (September 8, 2016): 1019–64. http://dx.doi.org/10.1017/s1474748016000232.

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Let $F$ be a unramified finite extension of $\mathbb{Q}_{p}$ and $\overline{\unicode[STIX]{x1D70C}}$ be an irreducible mod $p$ two-dimensional representation of the absolute Galois group of $F$. The aim of this article is the explicit computation of the Kisin variety parameterizing the Breuil–Kisin modules associated to certain families of potentially Barsotti–Tate deformations of $\overline{\unicode[STIX]{x1D70C}}$. We prove that this variety is a finite union of products of $\mathbb{P}^{1}$. Moreover, it appears as an explicit closed connected subvariety of $(\mathbb{P}^{1})^{[F:\mathbb{Q}_{p}]}$. We define a stratification of the Kisin variety by locally closed subschemes and explain how the Kisin variety equipped with its stratification may help in determining the ring of Barsotti–Tate deformations of $\overline{\unicode[STIX]{x1D70C}}$.
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Koch, Alan. "Breuil–Kisin Modules and Hopf Orders in Cyclic Group Rings." Communications in Algebra 40, no. 2 (February 2012): 607–31. http://dx.doi.org/10.1080/00927872.2010.535050.

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Ito, Kazuhiro. "On the Supersingular Reduction of K3 Surfaces with Complex Multiplication." International Mathematics Research Notices 2020, no. 20 (September 4, 2018): 7306–46. http://dx.doi.org/10.1093/imrn/rny210.

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Abstract We study the good reduction modulo $p$ of $K3$ surfaces with complex multiplication. If a $K3$ surface with complex multiplication has good reduction, we calculate the Picard number and the height of the formal Brauer group of the reduction. Moreover, if the reduction is supersingular, we calculate its Artin invariant under some assumptions. Our results generalize some results of Shimada for $K3$ surfaces with Picard number $20$. Our methods rely on the main theorem of complex multiplication for $K3$ surfaces by Rizov, an explicit description of the Breuil–Kisin modules associated with Lubin–Tate characters due to Andreatta, Goren, Howard, and Madapusi Pera, and the integral comparison theorem recently established by Bhatt, Morrow, and Scholze.
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Lau, Eike. "Dieudonné theory over semiperfect rings and perfectoid rings." Compositio Mathematica 154, no. 9 (August 17, 2018): 1974–2004. http://dx.doi.org/10.1112/s0010437x18007352.

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The Dieudonné crystal of a $p$-divisible group over a semiperfect ring $R$ can be endowed with a window structure. If $R$ satisfies a boundedness condition, this construction gives an equivalence of categories. As an application we obtain a classification of $p$-divisible groups and commutative finite locally free $p$-group schemes over perfectoid rings by Breuil–Kisin–Fargues modules if $p\geqslant 3$.
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Cais, Bryden, and Tong Liu. "Corrigendum to “Breuil–Kisin modules via crystalline cohomology"." Transactions of the American Mathematical Society 373, no. 3 (November 18, 2019): 2251–52. http://dx.doi.org/10.1090/tran/7894.

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Dissertations / Theses on the topic "Breuil-Kisin module"

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(10717026), Heng Du. "Arithmetic Breuil-Kisin-Fargues modules and several topics in p-adic Hodge theory." Thesis, 2021.

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Let K be a discrete valuation field with perfect residue field, we study the functor from weakly admissible filtered (φ,N,GK)-modules over K to the isogeny category of Breuil- Kisin-Fargues GK-modules. This functor is the composition of a functor defined by Fargues-Fontaine from weakly admissible filtered (φ,N,GK)-modules to GK-equivariant modifications of vector bundles over the Fargues-Fontaine curve XFF , with the functor of Fargues-Scholze that between the category of admissible modifications of vector bundles over XFF and the isogeny category of Breuil-Kisin-Fargues modules. We characterize the essential image of this functor and give two applications of our result. First, we give a new way of viewing the p-adic monodromy theorem of p-adic Galois representations. Also we show our theory provides a universal theory that enable us to compare many integral p-adic Hodge theories at the Ainf level.

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Book chapters on the topic "Breuil-Kisin module"

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Scholze, Peter, and Jared Weinstein. "The v-topology." In Berkeley Lectures on p-adic Geometry, 149–60. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691202082.003.0017.

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This chapter describes the v-topology. It develops a powerful technique for proving results about diamonds. There is a topology even finer than the pro-étale topology, the v-topology, which is reminiscent of the fpqc topology on schemes but which is more “topological” in nature. The class of v-covers is extremely general, which will reduce many proofs to very simple base cases. The chapter provides a sample application of this philosophy by establishing a general classification of p-divisible groups over integral perfectoid rings in terms of Breuil-Kisin-Fargues modules. Another use of the v-topology is to prove that certain pro-étale sheaves on Perf are diamonds without finding an explicit pro-étale cover.
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"Appendix F Breuil–Kisin–Fargues modules and potentially semistable representations (by Toby Gee and Tong Liu)." In Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts, 279–88. Princeton University Press, 2023. http://dx.doi.org/10.1515/9780691241364-014.

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