Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group

Sebastian Monnet

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arXiv · 2304.03154

Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group

Sebastian Monnet

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Abstract

Given a $2$-adic field $K$, we give formulae for the number of totally ramified quartic field extensions $L/K$ with a given discriminant valuation and Galois closure group. We use these formulae to prove a refinement of Serre's mass formula, which will have applications to the arithmetic statistics of number fields.

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Sebastian Monnet. 2023-04-06. Counting wildly ramified quartic extensions with prescribed discriminant and Galois closure group. https://arxiv.org/abs/2304.03154

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