## View abstract

### 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. document.getElementById('cloakbdfd983fb7ae7837f8615158f4507435').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addybdfd983fb7ae7837f8615158f4507435 = '&#97;lv&#97;r&#111;.l&#111;z&#97;n&#111;-r&#111;bl&#101;d&#111;' + '&#64;'; addybdfd983fb7ae7837f8615158f4507435 = addybdfd983fb7ae7837f8615158f4507435 + '&#117;c&#111;nn' + '&#46;' + '&#101;d&#117;'; var addy_textbdfd983fb7ae7837f8615158f4507435 = '&#97;lv&#97;r&#111;.l&#111;z&#97;n&#111;-r&#111;bl&#101;d&#111;' + '&#64;' + '&#117;c&#111;nn' + '&#46;' + '&#101;d&#117;';document.getElementById('cloakbdfd983fb7ae7837f8615158f4507435').innerHTML += '<a ' + path + '\'' + prefix + ':' + addybdfd983fb7ae7837f8615158f4507435 + '\'>'+addy_textbdfd983fb7ae7837f8615158f4507435+'<\/a>';

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.