## EVENT DETAILS AND ABSTRACT

**Number Theory**
**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.

**Date:** Friday, January 10, 2020

**Time:** 3:00PM

**Where:** Lunt 107

**Contact Person:** Bao Le Hung

**Contact email:** lhvietbao@math.northwestern.edu

**Contact Phone:**

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