**abstract:**
Let $E*\mathbf{Q}$ be an elliptic curve, let
$K*\mathbf{Q}$ be an imaginary quadratic field, and
let $p$ be a prime.
The anticyclotomic main conjectures of Iwasawa theory
--- formulated in different settings by Perrin-Riou and by Bertolini--Darmon --- relate the arithmetic properties of $E$ over the anticyclotomic $\mathbf{Z}_{p$}-extension $K_{{\infty}K$}* of $K$ to the special values of the Hasse--Weil $L$-function of $E*K$, twisted by finite order characters of the
Galois group of $K_{{\infty}K$.}*
I will report on a joint work with Massimo Bertolini,
in which we prove the
anticyclotomic main conjectures
for elliptic curves at primes of ordinary reduction.*

Wed 23 Sep, 15:30 - 15:55, Aula Contini

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