Iwasawa theory of overconvergent modular forms, I: Critical $p$-adic $L$-functions

David Hansen

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arXiv · 1508.03982

Iwasawa theory of overconvergent modular forms, I: Critical $p$-adic $L$-functions

David Hansen

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Abstract

We construct an Euler system of $p$-adic zeta elements over the eigencurve which interpolates Kato's zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable $p$-adic $L$-function over the eigencurve. As a first application of these ideas, we prove the equality of the $p$-adic $L$-functions associated with a critical-slope refinement of a modular form by the works of Bellaïche/Pollack-Stevens and Kato/Perrin-Riou.

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David Hansen. 2015-08-17. Iwasawa theory of overconvergent modular forms, I: Critical $p$-adic $L$-functions. https://arxiv.org/abs/1508.03982

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