The triple product Selmer group of an elliptic curve over a cubic real field

Mardi 10 octobre 14:15-15:15 - Yichao Tian - Hausdorff Center for Mathematics, Moringside Center of Mathematics

Résumé : Let F be a cubic totally real field, and E/F be a modular elliptic curve. We consider its triple product motive M attached to E, which is a 8-dimensional motive over Q. Assume that the functional equation of L(M,s) has sign -1. Under certain technical assumptions, one can construct a cohomology class in the p-adic Bloch-Kato Selmer group of M using Hirzebruch-Zagier cycles. We prove that if this class is non-trivial, then the Bloch-Kato Selmer group of M has dimension 1. A key ingredient in the proof is a congruence formula for the cohomology class at certain unramified level raising primes, whose proof uses the fine geometry of the supersingular locus of a Hilbert modular threefold at an inert prime. This is a joint work with Yifeng Liu.

Lieu : Bât. 425, salle 117-119 - Laboratoire de Mathématiques d’Orsay

The triple product Selmer group of an elliptic curve over a cubic real field  Version PDF