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

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.

arXiv commentFinal version accepted for publication in the Annales de l'Institut Fourier. Minor revisions. 11 pages