A main objective of algebraic number theory is to understand the absolute Galois group of the rational field. One way is to study its representations, called Galois representations. Algebro-geometric objects, such as abelian varieties, provide natural Galois representations which have been studied extensively in arithmetic geometry.

 

In this talk, I will discuss Galois representations arising from Jacobian varieties of curves, especially of small genus, and review recent results concerning the size of their image.