Session S09 - Number Theory in the Americas

Wednesday, July 14, 15:00 ~ 15:30 UTC-3

Towards a classification of adelic Galois representations attached to elliptic curves over ${\mathbb Q}$

Alvaro Lozano-Robledo

U. Connecticut, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Let $E$ be an elliptic curve defined over $\mathbb{Q}$. The adelic Galois representation attached to $E$ (this object will be defined during the talk) captures all sorts of interesting information about the arithmetic of the points on $E(\overline{\mathbb{Q}})$, including data about the torsion subgroup, isogenies, and other finer invariants of the curve and its isogeny class. In this talk, we will give a summary of recent results towards the classification (up to isomorphism) of the possible adelic Galois representations that arise from elliptic curves over $\mathbb{Q}$, and present some recent results of the author and his collaborators (Garen Chiloyan, Harris Daniels, Jackson Morrow) in this area.

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