The (negative) Artin conductor and minimal discriminant are two measures of bad reduction for a hyperelliptic curve over a discrete valuation field. Both are non-negative natural numbers, and are equal to 0 when the curve has good reduction. We show that, for residue characteristic not 2, the negative Artin conductor is bounded above by the minimal discriminant, which is much easier to compute.
This is joint work with Padmavathi Srinivasan and generalizes her work, as well as work of Ogg, Saito, and Liu in genus at most 2. The major innovation is the use of "Mac Lane" valuations, which the speaker learned from Stefan Wewers in the DRL tea room in April 2017.