Crystalline representations and F -crystals

By M. Kisin. 2006

237 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9f71f7471574a2f98061f7995fe2b0c38c0376cd

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Period spaces for Hodge structures in equal characteristic (2005, background): “If K is a finite extension of Qp with ring of integers OK , Breuil [Bre2, Théorème 1.4] (see also Kisin [Kis1, Theorem 0.3]) has shown that any crystalline representation of Gal(Ksep/K) with all Hodge-Tate weights equal to 0 or 1 arises from a p-divisible group over OK .”
A relation between Dieudonne displays and crystalline Dieudonne theory (2010, background): “6] for the Dieudonné crystal of a nilpotent display, and in [Kisin 2006; 2009] for p-divisible groups.”
Slope filtrations revisited (2005, methodology): “A variant of Berger’s proof has been given by Kisin [26], who goes on to give a classification of crystalline representations with nonpositive Hodge-Tate weights in terms of certain Frobenius modules; as corollaries, he obtains classification results for pdivisible groups conjectured by Breuil and F”
On the Averaged Colmez Conjecture (2015, methodology): “Now we would like to extend the groups I,H ′′ to integral models I,H′′ using Breuil– Kisin’s classification of p-divisible group [Ki1]: any crystalline representation of GK ∶= Gal(K̄ ′/K ′) of Hodge–Tate weights 0 or −1 arises from a p-divisible group over OK′ .”
Slope filtrations for relative Frobenius (2006, methodology): “otentially semistable [3] and to give an alternate proof of the Colmez-Fontaine theorem on admissibility of ﬁltered (φ,N)-modules [4]. (A useful variant of the latter argument has been given by Kisin [26].) More recently Colmez [11] used this viewpoint to deﬁne a class of trianguline representations”
Integral p$p$-adic Hodge theory (2016, unknown): “We note that the relation to shtukas has been emphasized by Kisin from the start, [48].”
Integral models for Shimura varieties of abelian type (2010, methodology): “The proposition is proved using the theory of our previous paper [Ki 1].”
Construction de (φ,Γ)-modules: représentations p-adiques et B-paires (2008, background): “Des objets de nature similaire ont été étudiés, dans un cadre un peu différent, dans [Kisin 2006].”