A p-adic Shimura-Maass operator on Mumford curves

Matteo Longo

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arXiv · 2011.05198

A p-adic Shimura-Maass operator on Mumford curves

Matteo Longo

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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.

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Matteo Longo. 2020-11-10. A p-adic Shimura-Maass operator on Mumford curves. https://arxiv.org/abs/2011.05198

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