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

2014; Association of the Annals of the Fourier Institute; Volume: 64; Issue: 6 Linguagem: Inglês

10.5802/aif.2916

1777-5310

Robert Harron, Liang Xiao,

Advanced Mathematical Identities

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.