Root numbers of abelian varieties

Given an abelian variety over a global field, one of its most interesting invariants is its rank. This is notoriously difficult to compute, so instead we simply ask: is the rank is odd or even? The answer to this is (conjecturally) encoded in the corresponding root number.

I will explore what information one needs to compute a root number and how to extract this data for hyperelliptic curves. As an application, we will produce an example such that every quadratic twist should have positive rank.