Number Theory Seminar
Fix a prime $\ell$ and an abelian variety $A$ over a number field. The Galois action on the torsion points of $A$ can be described by an $\ell$-adic Galois representation. The Zariski closure $G$ of its image is called the $\ell$-adic monodromy group of $A$. The group $G$ encodes a lot of the arithmetic/geometry of $A$. For example, the Sato–Tate distribution of $A$ can conjecturally be determined from $G$.
We will discuss approaches to studying and computing these monodromy groups.