Wild conductor exponents of curves

Abstract We give an explicit formula for wild conductor exponents of plane curves over in terms of standard invariants of explicit extensions of , generalising a formula for hyperelliptic curves. To do so, we prove a general result relating the wild conductor exponent of a simply branched cover of the projective line with its associated discriminant cover. In an Appendix, we resolve a minor issue in the literature on the 3‐torsion of genus 2 curves.