Conductors and minimal discriminants of hyperelliptic curves

Conductors and minimal discriminants are two measures of degeneracy of the singular fiber in a family of hyperelliptic curves. In genus one, the Ogg-Saito formula shows that these two invariants are equal, and in genus two, Qing Liu showed that they are related by an inequality. In this talk, we will show that Liu's inequality extends to hyperelliptic curves of arbitrary genus in odd residue characteristic. This is joint work with Andrew Obus.