Pip Goodman

Restrictions on endomorphism rings of hyperelliptic jacobians

Zarhin has given simple Galois theoretic conditions for the jacobian of a hyperelliptic curve to have trivial endomorphism ring. His result has seen applications in inverse Galois theory and algorithms for computing endomorphism algebras of hyperelliptic jacobians. The assumptions of this result require a certain Galois group to be "very big''.
In this talk, I will introduce and motivate the study of these objects, and examine what happens when we allow smaller Galois groups.