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

Robert HarronLiang Xiao — 2014

Annales de l’institut Fourier

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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