Honda-Tate theory for Shimura varieties

DOI10.1215/00127094-2021-0063OpenAlexW4226397632MaRDI QIDQ2671457

Mark Kisin, Sug Woo Shin, Keerthi Madapusi Pera

Publication date: 3 June 2022

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/duke-mathematical-journal/volume-171/issue-7/HondaTate-theory-for-Shimura-varieties/10.1215/00127094-2021-0063.full

zbMATH Keywords

abelian varietiesShimura varieties\(p\)-divisible groups

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items

\(H^0\) of Igusa varieties via automorphic forms, Connected components of affine Deligne–Lusztig varieties for unramified groups, Stratifications in the reduction of Shimura varieties, On supersingular loci of Shimura varieties for quaternionic unitary groups of degree 2, Strata Hasse invariants, Hecke algebras and Galois representations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stratifications in the reduction of Shimura varieties
• Galois representations arising from some compact Shimura varieties
• Existence of \(F\)-crystals with supplementary structures
• F-isocrystals and De Rham cohomology. I
• Stable trace formula: Elliptic singular terms
• F-isocrystals and de Rham cohomology. II: Convergent isocrystals
• Smoothness, semi-stability and alterations
• Propriétés du groupe tannakien des structures de Hodge \(p\)-adiques et torseur entre cohomologies cristalline et étale. (Properties of the Tannakian group of \(p\)-adic Hodge structures and torsor between crystalline and étale cohomologies.)
• Integral models of Shimura varieties with parahoric level structure
• Rational conjugacy classes in reductive groups
• Crystalline Dieudonné module theory via formal and rigid geometry
• Mod \(p\) isogeny classes on Shimura varieties with parahoric level structure
• \(l\)-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients
• Ekedahl-Oort and Newton strata for Shimura varieties of PEL type
• Endomorphisms of Abelian varieties over finite fields
• Über die Galoiskohomologie halbeinfacher Matrizengruppen II
• Nonemptiness of Newton strata of Shimura varieties of Hodge type
• Towards a theory of local Shimura varieties
• Mod $p$ points on Shimura varieties of abelian type
• Integral models for Shimura varieties of abelian type
• Connected components of affine Deligne–Lusztig varieties in mixed characteristic
• Classe de conjugaison du Frobenius d'une variété abélienne sur un corps de nombres
• Isogenieklassen von Punkten von SHIMURA mannigfaltigkeiten mit Werten in einem endlichen Körper
• Ordinariness in good reductions of shimura varieties of PEL-type
• Abelian Galois cohomology of reductive groups
• Points on Some Shimura Varieties Over Finite Fields
• Integral crystalline cohomology over very ramified valuation rings
• Some functional properties of the Bruhat-Tits building
• Toroidal compactifications of integral models of Shimura varieties of Hodge type
• Isogenies Between K3 Surfaces Over