Vendredi 14 Octobre

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Vendredi 14 Octobre
Heure: 10:30 - 12:00
Lieu: Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13
Résumé: Géométrie Arithmétique et Motivique - Supersingular main conjectures, Sylvester's conjecture and Goldfeld's conjecture -
Description: Daniel KrizI will present a rank 0 and 1 p-converse theorem for CM elliptic
curves defined over the rationals in the case where p is ramified in the
CM field. This theorem has applications to two classical problems of
arithmetic: it verifies Sylvester's conjecture on primes expressible as a
sum of two rational cubes and establishes Goldfeld's conjecture for the
congruent number family. The proof relies on formulating and proving a
new Iwasawa main conjecture, which in turn involves new methods arising
from interplays between Iwasawa-theoretic objects and relative p-adic
Hodge theory on the infinite-level Shimura curve.