Théorie de Dieudonné Cristalline II

Berthelot, Pièrre; Breen, Lawrence; Messing, William

doi:10.1007/bfb0093025

Cited by 213 publications

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“…In this section, we generalize to higher level the first results of the second chapter of [3]. The point is to describe the "mod p filtration on crystalline Dieudonné modules of level m" (Proposition 5.14).…”

Section: Gmmentioning

confidence: 93%

The Filtered Poincaré Lemma in Higher Level (With Applications to Algebraic Groups)

Stum¹,

Quirós²

2008

Nagoya Mathematical Journal

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Abstract. We show that the Poincaré lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincaré lemma for transversal crystals of level m. We interpret the de Rham complex in terms of what we call the Berthelot-Lieberman construction and show how the same construction can be used to study the conormal complex and invariant differential forms of higher level for a group scheme. Bringing together both instances of the construction, we show that crystalline extensions of transversal crystals by algebraic groups can be computed by reduction to the filtered de Rham complexes. Our theory does not ignore torsion and, unlike in the classical case (m = 0), not all invariant forms are closed. Therefore, close invariant differential forms of level m provide new invariants and we exhibit some examples as applications.

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Section: Gmmentioning

confidence: 93%

The Filtered Poincaré Lemma in Higher Level (With Applications to Algebraic Groups)

Stum¹,

Quirós²

2008

Nagoya Mathematical Journal

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“…Comme ces faisceaux sont quasi-cohérents ( [BBM,2.3.1]) et que E n est affine, on a encore une suite exacte avec les H 0 ((S/E n ) CRIS , −). Par (3.2.4) et (3.2.2), on en déduit une suite exacte comme dans l'énoncé.…”

Section: Schémas En Groupes De Type (P P)unclassified

“…Puisque S est le spectre d'un anneau local, par [BBM,3.1.1] il existe un S-schéma abélien A et une S-immersion fermée G 1 ֒→ A (c'est un cas particulier d'un théorème de Raynaud). Soit H le groupe p-divisible associéà A, alors H ′ = H/G 1 est encore un groupe p-divisible ( [BBM,3.3.12]), de sorte qu'on a une suite exacte pour la topologie fppf:…”

Section: Schémas En Groupes De Type (P P)unclassified

“…Soit H le groupe p-divisible associéà A, alors H ′ = H/G 1 est encore un groupe p-divisible ( [BBM,3.3.12]), de sorte qu'on a une suite exacte pour la topologie fppf:…”

Section: Schémas En Groupes De Type (P P)unclassified

“…( * , G a ) sontégaux aux Ext i correspondants calculés pour la topologie fppf ( [BBM,2.3.10,2.4.5,2.3.12 et 2.4.6]). On a donc un diagramme commutatif dans Ab S/E 1 :…”

Section: Schémas En Groupes De Type (P P)unclassified

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Groupes p-Divisibles, Groupes Finis et Modules Filtres

Breuil¹

2000

The Annals of Mathematics

110

127

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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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Théorie de Dieudonné Cristalline II

Cited by 213 publications

References 0 publications

The Filtered Poincaré Lemma in Higher Level (With Applications to Algebraic Groups)

The Filtered Poincaré Lemma in Higher Level (With Applications to Algebraic Groups)

Groupes p-Divisibles, Groupes Finis et Modules Filtres

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

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