An Example of Wild Ramification in an Enriched Riemann-Hurwitz Formula

Candace Bethea; Jesse Leo Kass; Kirsten Wickelgren

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arXiv · 1812.03386

An Example of Wild Ramification in an Enriched Riemann-Hurwitz Formula

Candace Bethea·Jesse Leo Kass·Kirsten Wickelgren

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Abstract

M. Levine proved an enrichment of the classical Riemann-Hurwitz formula to an equality in the Grothendieck-Witt group of quadratic forms. In its strongest form, Levine's theorem includes a technical hypothesis on ramification relevant in positive characteristic. We consider wild ramification at points whose residue fields are non-separable extensions of the ground field k. We show an analogous Riemann-Hurwitz formula, and consider an example suggested by S. Saito.

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Candace Bethea, Jesse Leo Kass, Kirsten Wickelgren. 2018-12-08. An Example of Wild Ramification in an Enriched Riemann-Hurwitz Formula. https://arxiv.org/abs/1812.03386

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