Iwasawa main conjecture for Rankin–Selberg p-adic L-functions

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

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 refin...

Hybrid Iwasawa Algebras and the Equivariant Iwasawa Main Conjecture

Let p be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for an infinite class of one-dimensional non-abelian p-adic Lie extensions. Crucially, this result does not depend on the vanishing of the relevant Iwasawa μ-invariant.

Cyclotomic Units and the Iwasawa Main Conjecture

In these notes, we follow the proof in [1] of the main conjecture of Iwasawa theory making heavy use of the Euler system of cyclotomic units. On the one hand, using the local theory of Coleman series and ideas of Iwasawa one obtains a connection with the p-adic zeta function. On the other hand by CFT and Rubin’s refinement of the ideas of Kolyvagin (and the analytic class number formula) one ob...

Equivariant Bloch-Kato conjecture and non-abelian Iwasawa Main Conjecture

In this talk we explain the relation between the (equivariant) Bloch-Kato conjecture for special values of L-functions and the Main Conjecture of (nonabelian) Iwasawa theory. On the way we will discuss briefly the case of Dirichlet characters in the abelian case. We will also discuss how “twisting” in the non-abelian case would allow to reduce the general conjecture to the case of number fields...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES