A geometric view on Iwasawa theory

2020/11/12 by Betina, Adel, Dimitrov, Mladen
#11F33 #11F80 #11R23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2011.06579

Abstract

This article extends our study of the geometry of the p-adic eigencurve at a point defined by a weight 1 cuspform f irregular at p and having complex multiplication, and the implications in Iwasawa and in Hida theories. The novel results include the determination of the Fourier coefficients of certain non-classical p-adic modular forms belonging to the generalized eigenspace of f, in terms of p-adic logarithms of algebraic numbers. We also compute the "mysterious" cross-ratios of the p-ordinary filtrations of the Hida families containing f.

Related

• Kida's formula and congruences
• Anticyclotomic p-ordinary Iwasawa Theory of Elliptic Modular Forms
• Iwasawa theory for symmetric powers of CM modular forms at nonordinary primes, II
• The Iwasawa Main Conjectures for \rm GL₂ and derivatives of p-adic L-functions
• Iwasawa theory of overconvergent modular forms, I: Critical p-adic L-functions