p-adic differential operators on automorphic forms, and mod p Galois representations

In this talk, we will discuss a geometric construction of p-adic analogues of Maass–Shimura differential operators on automorphic forms on Shimura varieties of PEL type A or C (that is, unitary or symplectic), at p an unramified prime. Maass–Shimura operators are smooth weight raising differential operators used in the study of special values of L-functions, and in the arithmetic setting for the construction of p-adic L-functions.  In this talk, we will focus in particular on the case of unitary groups of arbitrary signature, when new phenomena arise for p  non split.  We will also discuss an application to the study of modular mod p Galois representations. This talk is based on joint work with Ellen Eischen (in the unitary case for p non split), and with Eischen, Flanders, Ghitza, and Mc Andrew (in the other cases).

Zoom: https://harvard.zoom.us/j/96767001802

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