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

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.

30 pages; comments welcome

Cited by in corpus (6)

• Extended eigenvarieties for overconvergent cohomology
• Heegner points in Coleman families
• Interpolation of Beilinson-Kato elements and $p$-adic $L$-functions
• Zeta morphisms for rank two universal deformations
• Iwasawa Main Conjecture for $p$-adic families of elliptic modular cuspforms
• Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and the Perrin-Riou Conjecture