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arXiv · 2409.12688

Wild conductor exponents of curves

Harry Spencer
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Abstract

We give an explicit formula for wild conductor exponents of plane curves over $\mathbb{Q}_p$ in terms of standard invariants of explicit extensions of $\mathbb{Q}_p$, 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.

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Harry Spencer. 2024-09-19. Wild conductor exponents of curves. https://arxiv.org/abs/2409.12688

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