Reduction of Shimura varieties at parahoric levels

Reimann, Harry

doi:10.1007/s002290200244

Cited by 4 publications

(4 citation statements)

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“…(b) We say that a smooth O (v) -scheme Y of finite type is a Néron model of its generic fibre Y E(G,X) over O (v) , if for each smooth O (v) -scheme Z, every morphism Z E(G,X) → Y E(G,X) of E(G, X)-schemes extends uniquely to a morphism Z → Y of O (v) -schemes. Definition (a) is a variation of [Re2,Def. 1.5]; more precisely, the group G Z (p) (Z p ) is an h-hyperspecial subgroup of G Q p (Q p ) in the sense of loc.…”

Section: Definitions (A)mentioning

confidence: 99%

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Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

Vasiu¹

2007

Preprint

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We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0, p). As a first application we solve a conjecture of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic (0, p) of integral canonical models of projective Shimura varieties of Hodge type; this forms progress towards the proof of conjectures of Milne and Reimann. Though the second application was known before in some cases, its proof is new and more of a principle.

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Section: Definitions (A)mentioning

confidence: 99%

“…Besides their applications to the conjecture of Langlands, Theorems 1.5 and 1.7 are also key steps in proving the deep conjectures [Re1,Conjs. B 3.7 and B 3.12] and [Re2,Conj. 1.6].…”

Section: Definitions (A)mentioning

confidence: 99%

Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

Vasiu¹

2007

Preprint

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“…Definition 1.2 (a) is a variation of [51, Def. 1.5]; more precisely, the group

G_{Z_{false(p false)}} (Z_{p})

is an h‐hyperspecial subgroup of

G_{Q_{p}} true(Q_{p} true)

in the sense of loc.…”

Section: Introductionmentioning

confidence: 99%

“…Besides their applications to the conjecture of Langlands, Theorems 1.3 and 1.7 are also key steps in proving the deep conjectures [50, Conjs. B 3.7 and B 3.12] and [51, Conj. 1.6].…”

Section: Introductionmentioning

confidence: 99%

Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

Vasiu

2020

Mathematische Nachrichten

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We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0,). As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic (0,) of integral canonical models of projective Shimura varieties of Hodge type with respect to h-hyperspecial subgroups as pro-étale covers of Néron models; this forms progress towards the proof of conjectures of Milne and Reimann. Though the second application was known before in some cases, its proof is new and more of a principle.

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Cohomology of quaternionic Shimura varieties at parahoric levels

Reimann¹

2002

manuscripta mathematica

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Reduction of Shimura varieties at parahoric levels

Cited by 4 publications

References 3 publications

Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

Cohomology of quaternionic Shimura varieties at parahoric levels

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