Hecke operators and the coherent cohomology of Shimura varieties

Abstract

We consider the problem of defining an action of Hecke operators on the coherent cohomology of certain integral models of Shimura varieties. We formulate a general conjecture describing which Hecke operators should act integrally and solve the conjecture in certain cases. As a consequence, we obtain $p$-adic estimates of Satake parameters of certain non-regular self dual automorphic representations of ${\mathrm{GL}}_n$.

References in corpus (2)

• Normality and Cohen-Macaulayness of local models of Shimura varieties
• Coherent cohomology of Shimura varieties and automorphic forms

Cited by in corpus (5)

• Higher Hida theory and p-adic L-functions for GSp(4)
• Higher Hida and Coleman theories on the modular curve
• Entire theta operators at unramified primes
• Compactifications of Iwahori-level Hilbert modular varieties
• Kodaira-Spencer isomorphisms and degeneracy maps on Iwahori-level Hilbert modular varieties: the saving trace