Integral models for Shimura varieties of abelian type

By M. Kisin. 2010

289 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cc043c40dd970c0a17e14eaff0da7fa7ca7eb92e

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the Averaged Colmez Conjecture (2015, background): “h a surjective map SÐ→O L by sending uto a uniformizer πL of L, then D(G) = OL⊗ Sϕ∗MT(G). where MisafunctorfromRepcriso GL tocertain categoryModϕ S ofmodules over non-commutative ring S[ϕ], deﬁned in [Ki2], Theorem 1.2.1. Applying this to divisible groups H′′ x′′, (Hx)O K′ , Iz over OL = OK′, and ta”
Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type (2013, methodology): “Here we collect some of the main results in [9].”
Strata Hasse invariants, Hecke algebras and Galois representations (2015, methodology): “ere he introduces the general framwork of PEL-type Shimura varieties and constructs models at primes of good reduction. This construction was then generalized by Kisin-Vasiu to the Hodge-type case in [Kis10] and [Vas99]. The special ﬁber of the Shimura variety is then a smooth quasi-projective schem”
The Tate conjecture for K3 surfaces in odd characteristic (2013, background): “It does not require any of the more advanced machinery in [21] and reduces to a statement that can be found in [20].”
Integral models of Shimura varieties with parahoric level structure (2015, methodology): “However, for more general parahoric level structures Kp, many of the key arguments of [41] break down or become much more complicated.”
Rapoport–Zink spaces for spinor groups (2015, methodology): “hat k′/kis ﬁnitely generated, by a simpler version of the above argument. 3. Shimura varieties and representability 3.1. Integral models of Shimura varieties of Hodge type. Here, we recall results of [Kis10] about integral models of Shimura varieties of Hodge type. We actually follow the set-up of [”
Semistable Higgs bundles, periodic Higgs bundles and representations of algebraic fundamental groups (2013, methodology): “Σ be the set of ﬁnite primes of F. For a prime p∈ Σ, let f0 p : A 0 p → M 0 p be the completion of fover p. In order to get a reasonable integrable model of f0 p, we shall invoke the work of M. Kisin [17]. This step has been done in [36, §2] and shall not be reproduced here but simply stating that, ”
Integral canonical models for Spin Shimura varieties (2012, methodology): “the case of Shimura curves, cf. [KRY06], and for the case of certain HilbertBlumenthalsurfaces, cf. [DP94,KR99]. Moreover,there isworkin progressbyKisinandPappas, which will generalize the methods of [Kis10] to construct integral models of Shimura varieties of abelian type with general parahoric lev”
2-ADIC INTEGRAL CANONICAL MODELS (2016, methodology): “Moreover, they can be used to support Kisin’s proof of the Langlands–Rapoport conjecture [13] for Shimura varieties of abelian type even at the 2-adic places.”