## On base change of family of p-adic automorphic forms

**Speaker(s): ** Zhengyu Xiang (Shanghai Center for Mathematical Sciences & Fudan University)

**Time: ** 00:00-00:00 January 8, 2015

**Venue: ** Room 09 at Quan Zhai, BICMR

Speaker: Zhengyu Xiang (Shanghai Center for Mathematical Sciences & Fudan University)

Time: Jan 08, 2015 Thursday 14:00-16:00

Place: Room 9 at Quan Zhai, BICMR

Abstract: Let $F$ be a totally real field and $E/F$ a cyclic extension such that $Gal(E/F)=<\sigma>$. Let $G$ be a reductive group over $F$. We set up a "trace formula" type equation for finite slope character distributions under the assumption of some results of classical base change theory. Then we can prove that there is an analytic map from the eigenvariety of $G_/F$ to the eigenvariety of $G_/E$. It gives a base change lifting of a family of p-adic automorphic forms of $G_/F$ to a family of $\sigma$-stable p-adic automorphic forms of $G_/E$.