## View abstract

### Session S21 - Galois representations and automorphic forms

Thursday, July 15, 14:05 ~ 14:45 UTC-3

## p-adic families of Yoshida lifts

### Zheng Liu

#### University of California, Santa Barbara, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak5537cc37867a1be0452d3ece8ed52564').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy5537cc37867a1be0452d3ece8ed52564 = 'zl&#105;&#117;' + '&#64;'; addy5537cc37867a1be0452d3ece8ed52564 = addy5537cc37867a1be0452d3ece8ed52564 + 'm&#97;th' + '&#46;' + '&#117;csb' + '&#46;' + '&#101;d&#117;'; var addy_text5537cc37867a1be0452d3ece8ed52564 = 'zl&#105;&#117;' + '&#64;' + 'm&#97;th' + '&#46;' + '&#117;csb' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak5537cc37867a1be0452d3ece8ed52564').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy5537cc37867a1be0452d3ece8ed52564 + '\'>'+addy_text5537cc37867a1be0452d3ece8ed52564+'<\/a>';

We construct a Hida family of Yoshida lifts for two given Hida families of modular forms, and compute the Petersson inner products of its specializations. The key step in the construction is to choose suitable Schwartz functions at $p$. The computation of the Petersson inner products can be viewed as a generalization of the computation in the works by Bocherer--Dummigan--Schulze-Pillot and Hsieh--Namikawa. Our computation makes use of an equivariant property of the chosen Schwartz functions at $p$ for the action of $U_p$ operators. This is an ongoing joint work with Ming-Lun Hsieh.

Joint work with Ming-Lun Hsieh (Academia Sinica).