A p-adic Shimura-Maass operator on Mumford curves

Abstract

We study a p-adic Shimura-Maass operator in the context of Mumford curves defined by C. Franc is his Ph.D. Thesis. We prove that this operator arises from a splitting of the Hodge filtration, thus answering a question in Franc. We also study the relation of this operator with generalized Heegner cycles, in the spirit of Bertolini-Darmon-Prasanna and Brooks.