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arXiv · 1308.1732

Gauss-Manin connections for p-adic families of nearly overconvergent modular forms

Robert Harron·Liang Xiao
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Abstract

We interpolate the Gauss-Manin connection in p-adic families of nearly overconvergent modular forms. This gives a family of Maass-Shimura type differential operators from the space of nearly overconvergent modular forms of type r to the space of nearly overconvergent modular forms of type r + 1 with p-adic weight shifted by 2. Our construction is purely geometric, using Andreatta-Iovita-Stevens and Pilloni's geometric construction of eigencurves, and should thus generalize to higher rank groups.

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BibTeXRIS

Robert Harron, Liang Xiao. 2014-07-15. Gauss-Manin connections for p-adic families of nearly overconvergent modular forms. https://arxiv.org/abs/1308.1732

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