Abstract

AbstractWe 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 nonregular self-dual automorphic representations of $\mathrm {GL}_n$ .

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