Twisted Triple Product p-adic L-function for Finite Slope Families of Hilbert Modular Forms

2024/01/24 by Kazi, Ananyo
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.13230

Abstract

Let L be a totally real field, and p be a rational prime that is unramified in L. We construct overconvergent families of classes of relative de Rham cohomology of the universal abelian scheme over Hilbert modular varieties associated to L. We show that these classes come equipped with Gauss-Manin connection. We prove convergence for p-adic iteration of this connection, improving upon a technique due to Andreatta-Iovita. We use this to construct a p-adic twisted triple product L-function associated to finite slope families of Hilbert modular forms, extending work of Blanco-Chacon-Fornea for Hida families.

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