EVENT DETAILS AND ABSTRACT

Title: Independence of $l$ for Frobenius conjugacy classes attached to abelian varieties.
Speaker: Rong Zhou
Speaker Info: Yale
Brief Description:
Special Note:
Abstract:

Let $A$ be an abelian variety over a number field $E\subset \mathbb{C}$. For $l$ a prime, a result of Deligne implies that upon replacing $E$ by a finite extension, we obtain a representation $\rho_l:\mathrm{Gal}(\overline{E}/E)\rightarrow G(\mathbb{Q}_l)$ where $G$ is the Mumford--Tate group of $A$. For $v\nmid l$ a prime of $E$ where $A$ has good reduction, we show that the conjugacy class of $\rho_l(\mathrm{Frob}_v)$ in $G(\mathbb{Q}_l)$ is defined over $\mathbb{Q}$ and is independent of $l$. This is joint work with Mark Kisin.