Sous-groupes canoniques et cycles évanescents p-adiques pour les variétés abéliennes

Abbes, Ahmed; Mokrane, Abdellah

doi:10.1007/s10240-004-0022-x

Cited by 38 publications

(102 citation statements)

References 32 publications

(27 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Before going on, let us recall the description of these Hecke algebras, and define some elements in these algebras. 2 Curiously, the Galois representations we need are the ones that are hardest to construct: They are regular, but non-Shin-regular, and not of finite slope at p.…”

Section: Galois Representations V1 Recollectionsmentioning

confidence: 99%

“…Let G be a group giving rise to a (connected) Shimura variety of Hodge type (thus, we allow Sp 2g , not only GSp 2g ), and let S K , K ⊂ G(A f ) be the associated Shimura variety over C. 2 Recall the definition of the (compactly supported) completed cohomology groups for a tame level…”

Section: Introductionmentioning

confidence: 99%

“…Then the second key ingredient is the following theorem. 2 We need not worry about fields of definition by fixing an isomorphism C ∼ = Q p . 3 These results are still conditional on the stabilization of the twisted trace formula, but compare the recent work of Waldspurger and Moeglin, [47].…”

Section: Introductionmentioning

confidence: 99%

“…e.g. [46], [43], [2], [3], [24], [31], [35], [52], [62]; however, not the whole canonical tower is overconvergent. By contrast, the whole anticanonical tower is overconvergent.…”

Section: Iii1 Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On torsion in the cohomology of locally symmetric varieties

Scholze

2015

Ann. Math.

130

View full text Add to dashboard Cite

Abstract. The main result of this paper is the existence of Galois representations associated with the mod p (or mod p m ) cohomology of the locally symmetric spaces for GL n over a totally real or CM field, proving conjectures of Ash and others. Following an old suggestion of Clozel, recently realized by Harris-Lan-Taylor-Thorne for characteristic 0 cohomology classes, one realizes the cohomology of the locally symmetric spaces for GL n as a boundary contribution of the cohomology of symplectic or unitary Shimura varieties, so that the key problem is to understand torsion in the cohomology of Shimura varieties.Thus, we prove new results on the p-adic geometry of Shimura varieties (of Hodge type). Namely, the Shimura varieties become perfectoid when passing to the inverse limit over all levels at p, and a new period map towards the flag variety exists on them, called the Hodge-Tate period map. It is roughly analogous to the embedding of the hermitian symmetric domain (which is roughly the inverse limit over all levels of the complex points of the Shimura variety) into its compact dual. The Hodge-Tate period map has several favorable properties, the most important being that it commutes with the Hecke operators away from p (for the trivial action of these Hecke operators on the flag variety), and that automorphic vector bundles come via pullback from the flag variety.

show abstract

Section: Galois Representations V1 Recollectionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…e.g. [46], [43], [2], [3], [24], [31], [35], [52], [62]; however, not the whole canonical tower is overconvergent. By contrast, the whole anticanonical tower is overconvergent.…”

Section: Iii1 Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On torsion in the cohomology of locally symmetric varieties

Scholze

2015

Ann. Math.

130

View full text Add to dashboard Cite

show abstract

“…The dimension one case played a fundamental role in the pioneering work of Katz on p-adic modular forms [14]. For higher-dimensional abelian schemes, Dwork's conjecture was first solved by Abbes and Mokrane [1]; our approach is a generalization of their results. Later, there have been other proofs, 1.3.…”

mentioning

confidence: 93%

Canonical subgroups of Barsotti-Tate groups

Tian

2010

Ann. Math.

View full text Add to dashboard Cite

Let S be the spectrum of a complete discrete valuation ring with fraction field of characteristic 0 and perfect residue field of characteristic p 3. Let G be a truncated Barsotti-Tate group of level 1 over S . If "G is not too supersingular", a condition that will be explicitly expressed in terms of the valuation of a certain determinant, then we prove that we can canonically lift the kernel of the Frobenius endomorphism of its special fiber to a subgroup scheme of G, finite and flat over S . We call it the canonical subgroup of G.

show abstract

Canonical subgroups via Breuil–Kisin modules

Hattori

2012

Math. Z.

View full text Add to dashboard Cite

Abstract. Let p > 2 be a rational prime and K/Qp be an extension of complete discrete valuation fields. Let G be a truncated BarsottiTate group of level n, height h and dimension d over OK with 0 < d < h. In this paper, we show that if the Hodge height of G is less than 1/(p n−2 (p + 1)), then there exists a finite flat closed subgroup scheme of G of order p nd over OK with standard properties as the canonical subgroup.

show abstract

Sous-groupes canoniques et cycles évanescents p-adiques pour les variétés abéliennes

Cited by 38 publications

References 32 publications

On torsion in the cohomology of locally symmetric varieties

On torsion in the cohomology of locally symmetric varieties

Canonical subgroups of Barsotti-Tate groups

Canonical subgroups via Breuil–Kisin modules

Contact Info

Product

Resources

About