Triple product p-adic L-functions associated to finite slope p-adic families of 
modular forms (Appendix by Eric Urban)

Andreatta, Fabrizio; Iovita, Adrian

doi:10.1215/00127094-2020-0076

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Triple product p-adic L-functions associated to finite slope p-adic families of modular forms (Appendix by Eric Urban)

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Iovita, Adrian
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1215/00127094-2020-0076
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https://doi.org/10.48550/arXiv.1708.02785
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Citation

Andreatta, F., & Iovita, A. (2021). Triple product p-adic L-functions associated to finite slope p-adic families of modular forms (Appendix by Eric Urban). Duke Mathematical Journal, 170(9), 1989-2083. doi:10.1215/00127094-2020-0076.

Cite as: https://hdl.handle.net/21.11116/0000-0008-FD5E-3

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.