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arXiv · 1910.03790

Hecke operators and the coherent cohomology of Shimura varieties

Najmuddin Fakhruddin·Vincent Pilloni
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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 $\mathrm{GL}_n$.

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Najmuddin Fakhruddin, Vincent Pilloni. 2019-10-09. Hecke operators and the coherent cohomology of Shimura varieties. https://doi.org/10.1017/s1474748021000050

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