Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms.
Gauss–Manin connections for -adic families of nearly overconvergent modular forms
We interpolate the Gauss–Manin connection in -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 to the space of nearly overconvergent modular forms of type with -adic weight shifted by . Our construction is purely geometric, using Andreatta–Iovita–Stevens and Pilloni’s geometric construction of eigencurves, and should thus generalize to higher rank groups.
Gauss's ₂F₁ hypergeometric function and the congruent number elliptic curve
Geometric and -adic Modular Forms of Half-Integral Weight
In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define -adic modular forms of half-integral weight and to construct -adic Hecke operators.