0 Introduction The central point in the Bloch-Kato conjectures is to establish formulas for the order of the Selmer groups attached to Galois representations in terms of the special values of their L-functions. In order to give upper bound, the main way is to construct Euler systems following Kolyvagin. Besides, lower bounds have been obtained by using congruences between automorphic forms. So,...

Norm-compatible families of cohomology classes for Shimura varieties, and other arithmetic symmetric spaces, play an important role in Iwasawa theory automorphic forms. The aim this note is to give a systematic approach proving “vertical” norm-compatibility relations such (where the level varies at fixed prime p), treating case Betti étale once, revealing unexpected relation spherical varieties...

The Tamagawa number conjecture proposed by S. Bloch and K. Kato describes the “special values” of L-functions in terms of cohomological data. The main conjecture of Iwasawa theory describes a p-adic L-function in terms of the structure of modules for the Iwasawa algebra. We give a complete proof of both conjectures (up to the prime 2) for L-functions attached to Dirichlet characters. We use the...

We construct an analogue of the Stickelberger ideal for real abelian fields by means of cyclotomic units and a Kummer-type pairing with values in a completed p-adic group-ring. We give several different descriptions of this ideal, prove the analogue of Stickelberger's Theorem using Thaine's methods and establish links with certain Fitting ideals in a particular case. Our construction fits into ...

Let $E/\mathbf{Q}$ be an elliptic curve of conductor $N$, let $p>3$ a prime where $E$ has good ordinary reduction, and $K$ imaginary quadratic field satisfying the Heegner hypothesis. In 1987, Perrin-Riou formulated Iwasawa main conjecture for Tate-Shafarevich group over anticyclotomic $\mathbf{Z}_p$-extension in terms points. this paper, we give proof Perrin-Riou's under mild hypotheses. Our b...