Simone Muselli

Regular models of hyperelliptic curves

To describe the arithmetic of curves over Q (or other global fields), for example in the study of the Birch & Swinnerton-Dyer conjecture, it is essential to understand regular models over all primes p, including those with very bad reduction. Constructing regular models of curves is not an easy problem, even in the hyperelliptic curve case.In the first part of this talk we will give an introduction to regular models of curves. We will then restrict to hyperelliptic curves, presenting the previous works and our new result (work in progress) that constructs a regular model of any hyperelliptic curve when p is not 2.