# Generalized Heegner cycles on Mumford curves

@article{Longo2019GeneralizedHC,
title={Generalized Heegner cycles on Mumford curves},
author={Matteo Longo and Maria Rosaria Pati},
journal={Mathematische Zeitschrift},
year={2019},
volume={297},
pages={483-515}
}
• Published 1 June 2019
• Mathematics
• Mathematische Zeitschrift
We study generalised Heegner cycles, originally introduced by Bertolini–Darmon–Prasanna for modular curves in Bertolini et al. (Duke Math J 162(6):1033–1148, 2013), in the context of Mumford curves. The main result of this paper relates generalized Heegner cycles with the two variable anticyclotomic p -adic L -function attached to a Coleman family $$f_\infty$$ f ∞ and an imaginary quadratic field K , constructed in Bertolini and Darmon (Invent Math 168(2):371–431, 2007) and Seveso (J Reine…
1 Citations
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

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