Third Italian Number Theory Meeting

# The anticyclotomic main conjecture for elliptic curves

speaker: Rodolfo Venerucci (University of Duisburg-Essen)

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 $EK$, 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.

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