Clusters, inertia, and root numbers

Matthew Bisatt

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arXiv · 1902.08981

Clusters, inertia, and root numbers

Matthew Bisatt

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Abstract

In a recent paper of Dokchitser--Dokchitser--Maistret--Morgan, the authors introduced the concept of a cluster picture associated to a hyperelliptic curve from which they are able to recover numerous invariants, including the inertia representation on the first \'{e}tale cohomology group of the curve. The purpose of this paper is to explore the functionality of these cluster pictures and prove that the inertia representation of a hyperelliptic curve is a function of its cluster picture.

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Matthew Bisatt. 2019-02-24. Clusters, inertia, and root numbers. https://arxiv.org/abs/1902.08981

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