## View abstract

### Session S21 - Galois representations and automorphic forms

Thursday, July 15, 12:00 ~ 12:40 UTC-3

## Iwasawa theory for ${\rm GL}_2\times{\rm GL}_2$ and diagonal cycles

### Francesc Castella

#### University of California, Santa Barbara, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak1b56e43db96032d6097c461abb6ae612').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy1b56e43db96032d6097c461abb6ae612 = 'c&#97;st&#101;ll&#97;' + '&#64;'; addy1b56e43db96032d6097c461abb6ae612 = addy1b56e43db96032d6097c461abb6ae612 + '&#117;csb' + '&#46;' + '&#101;d&#117;'; var addy_text1b56e43db96032d6097c461abb6ae612 = 'c&#97;st&#101;ll&#97;' + '&#64;' + '&#117;csb' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak1b56e43db96032d6097c461abb6ae612').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy1b56e43db96032d6097c461abb6ae612 + '\'>'+addy_text1b56e43db96032d6097c461abb6ae612+'<\/a>';

In this talk I will explain the construction, in joint work with Raul Alonso Rodriguez and Oscar Rivero, of an anticyclotomic Euler system for the tensor product of the Galois representations attached to two modular forms arising from generalized Gross--Kudla--Schoen diagonal cycles and their variation in $p$-adic families. As applications of this construction, we prove new cases of the Bloch--Kato conjecture in analytic rank zero and a divisibility towards an Iwasawa main conjecture.