Vanishing results for the coherent cohomology of automorphic vector bundles over the Siegel variety in positive characteristic

DOI10.2140/ANT.2025.19.143MaRDI QIDQ6652392

Thibault Alexandre

Publication date: 12 December 2024

Published in: Algebra \& Number Theory (Search for Journal in Brave)

zbMATH Keywords

Shimura varietiespositive characteristichighest weightautomorphic representationsabelian schemesWeyl chambercoherent cohomologySiegel modular varietyvanishing resultsautomorphic vector bundlessagemathSiegel varietyg-zip theory.

Mathematics Subject Classification ID

Modular and Shimura varieties (14G35)

Cites Work

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• Vanishing theorems for torsion automorphic sheaves on general PEL-type Shimura varieties
• Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties
• Algebraic zip data
• Toroidal embeddings. I
• Rational representations of algebraic groups: Tensor products and filtrations
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• Relèvements modulo \(p^ 2\) et décomposition du complexe de de Rham. (Lifting modulo \(p^ 2\) and decomposition of the de Rham complex)
• Toroidal compactifications of PEL-type Kuga families
• Strata Hasse invariants, Hecke algebras and Galois representations
• \(F\)-zips with additional structure
• Equations différentielles à points singuliers réguliers
• On two mod \(p\) period maps: Ekedahl-Oort and fine Deligne-Lusztig stratifications
• Ordinariness in good reductions of shimura varieties of PEL-type
• Filtrations of $G$-modules
• Stratifications of Flag Spaces and Functoriality
• Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type

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