Adam Morgan: Invariants of hyperelliptic curves over local fields

Let \(C:y^2 = f(x)\) be a hyperelliptic curve over a local field of odd residue characteristic. I will present joint work with Tim and Vladimir Dokchitser, and Celine Maistret, demonstrating how several arithmetic invariants of the curve and its Jacobian, including its potential stable reduction, Galois representation, and (in the semistable case) Tamagawa numbers, can be described in terms of simple combinatorial data involving the \(p\)-adic distances between the roots of \(f(x)\).