Triple product p-adic L-functions associated to finite slope p-adic families of modular forms, with an appendix by Eric Urban

Abstract

We p-adically interpolate the relative de Rham cohomology of the universal elliptic curve over strict neighbourhoods of the ordinary locus of modular curves, together with the Hodge filtration and Gauss-Manin connection. Sections of these sheaves provide the so called nearly overconvergent modular forms. This extends previous work of Andreatta, Iovita and Pilloni where we p-adically interpolate powers of the Hodge bundle and in that case the sections coincide with Coleman overconvergent modular forms. We also show that, under suitable assumptions, one can p-adically interpolate the Gauss-Manin connection. This is used to define p-adic L-functions attached to a triple of p-adic finite slope families of modular forms, generalizing previous constructions for Hida families.

Cited by in corpus (6)

• Rankin--Eisenstein classes for modular forms
• Higher Hida theory and p-adic L-functions for GSp(4)
• Iwasawa theory for Rankin--Selberg products of $p$-non-ordinary eigenforms
• Katz type p-adic L-functions for primes p non-split in the CM field
• P-adic L-functions in universal deformation families
• Iwasawa theory for $\mathrm{U}(r,s)$, Bloch-Kato conjecture and Functional Equation