Cohomologie cohérente et représentations Galoisiennes

Pilloni, Vincent; Stroh, Benoît

doi:10.1007/s40316-015-0056-0

Cited by 31 publications

(54 citation statements)

References 19 publications

(7 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…I.3.1 and Th. I.3.2 were obtained simultaneously and independently by Pilloni-Stroh [86]. Their method is completely different: It is based on Scholze's theory of perfectoid Shimura varieties.…”

Section: Introductionmentioning

confidence: 99%

Strata Hasse invariants, Hecke algebras and Galois representations

Goldring

Koskivirta

2019

Invent. math.

View full text Add to dashboard Cite

We construct group-theoretical generalizations of the Hasse invariant on strata closures of the stacks G-Zip µ . Restricting to zip data of Hodge type, we obtain a group-theoretical Hasse invariant on every Ekedahl-Oort stratum closure of a general Hodge-type Shimura variety. A key tool is the construction of a stack of zip flags G-ZipFlag µ , fibered in flag varieties over G-Zip µ . It provides a simultaneous generalization of the "classical case" homogeneous complex manifolds studied by Griffiths-Schmid and the "flag space" for Siegel varieties studied by Ekedahl-van der Geer.Four applications are obtained: (1) Pseudo-representations are attached to the coherent cohomology of Hodgetype Shimura varieties modulo a prime power. (2) Galois representations are associated to many automorphic representations with non-degenerate limit of discrete series archimedean component. (3) It is shown that all Ekedahl-Oort strata in the minimal compactification of a Hodge-type Shimura variety are affine, thereby proving a conjecture of Oort. (4) Part of Serre's letter to Tate on mod p modular forms is generalized to general Hodge-type Shimura varieties.

show abstract

Section: Introductionmentioning

confidence: 99%

Strata Hasse invariants, Hecke algebras and Galois representations

Goldring

Koskivirta

2019

Invent. math.

View full text Add to dashboard Cite

show abstract

“…The results of the present section are entirely due to Scholze [Sch15], then to Caraiani-Scholze [CS17] and Pilloni-Stroh [PS16].…”

Section: B Perfectoid Shimura Varieties and The Hodge-tate Morphismmentioning

confidence: 55%

“…The following theorem is essentially due to Pilloni and Stroh. In [PS16] this is proved for the Siegel modular variety, although it is not stated in this form. In Section 5 we explain their result and show how to obtain Theorem 2.22 for general Shimura varieties of Hodge type, under Hypothesis 2.18.…”

Section: B Perfectoid Shimura Varieties and The Hodge-tate Morphismmentioning

confidence: 99%

See 1 more Smart Citation

Chern classes of automorphic vector bundles

Esnault

Harris

2017

Pure and Applied Mathematics Quarterly

View full text Add to dashboard Cite

We prove that the -adic Chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of Shimura varieties of Hodge type overQ p , descend to classes in the -adic cohomology of the minimal compactifications. These are invariant under the Galois group of the p-adic field above which the variety and the bundle are defined. [Français]Titre. Classes de Chern des fibrés vectoriels automorphes, II Résumé. Nous démontrons que, sur les compactifications toroïdales des variétés de Shimura de type Hodge surQ p , les classes de Chern -adiques des extensions canoniques des fibrés vectoriels automorphes descendent en des classes de cohomologie -adique sur les compactifications minimales. Elles sont invariantes sous l'action du groupe de Galois du corps p-adique sur lequel la variété et le fibré sont définis.

show abstract

“…Remark 2.7. In certain cases, Galois representations have been constructed for irregular π (see, in particular, the recent papers of [15,23] in the case that the descent of π to a unitary group has a non-degenerate limit of discrete series as archimedean component). In Theorem 4.1, we consider representations that are residually reducible and not necessarily Hodge-Tate regular (for an example see [4, Theorem 5.1]).…”

Section: Polarized Galois Representations and Signsmentioning

confidence: 99%

Oddness of residually reducible Galois representations

Berger

2018

Int. J. Number Theory

View full text Add to dashboard Cite

We show that suitable congruences between polarized automorphic forms over a CM field always produce elements in the Selmer group for exactly the ±-Asai (aka tensor induction) representation that is critical in the sense of Deligne. For this, we relate the oddness of the associated polarized Galois representations (in the sense of the Bellaïche-Chenevier sign being +1) to the parity condition for criticality. Under an assumption similar to Vandiver's conjecture this also provides evidence for the Fontaine-Mazur conjecture for residually reducible polarized Galois representations.

show abstract

Cohomologie cohérente et représentations Galoisiennes

Cited by 31 publications

References 19 publications

Strata Hasse invariants, Hecke algebras and Galois representations

Strata Hasse invariants, Hecke algebras and Galois representations

Chern classes of automorphic vector bundles

Oddness of residually reducible Galois representations

Contact Info

Product

Resources

About