Quotients of hyperelliptic curves and Étale cohomology

Tim Dokchitser; Vladimir Dokchitser

doi:10.1093/qmath/hax053

Quotients of hyperelliptic curves and Étale cohomology

Tim Dokchitser, Vladimir Dokchitser^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We study hyperelliptic curves C with an action of an affine group of automorphisms G. We establish a closed form expression for the quotient curve C/G and for the first étale cohomology group of C as a representation of G. The motivation comes from the arithmetic of hyperelliptic curves over local fields, specifically their local Galois representations and the associated invariants.

Original language	English
Pages (from-to)	747-768
Number of pages	22
Journal	Quarterly Journal of Mathematics
Volume	69
Issue number	2
Early online date	8 Feb 2018
DOIs	https://doi.org/10.1093/qmath/hax053
Publication status	Published - 1 Jun 2018

Keywords

hyperelliptic curves
quotient curves
etale cohomology
Galois representations

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10.1093/qmath/hax053

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Oxford Academic at https://academic.oup.com/qjmath/article/69/2/747/4844050 . Please refer to any applicable terms of use of the publisher.
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abstract = "We study hyperelliptic curves C with an action of an affine group of automorphisms G. We establish a closed form expression for the quotient curve C/G and for the first {\'e}tale cohomology group of C as a representation of G. The motivation comes from the arithmetic of hyperelliptic curves over local fields, specifically their local Galois representations and the associated invariants.",

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AU - Dokchitser, Vladimir

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N2 - We study hyperelliptic curves C with an action of an affine group of automorphisms G. We establish a closed form expression for the quotient curve C/G and for the first étale cohomology group of C as a representation of G. The motivation comes from the arithmetic of hyperelliptic curves over local fields, specifically their local Galois representations and the associated invariants.

AB - We study hyperelliptic curves C with an action of an affine group of automorphisms G. We establish a closed form expression for the quotient curve C/G and for the first étale cohomology group of C as a representation of G. The motivation comes from the arithmetic of hyperelliptic curves over local fields, specifically their local Galois representations and the associated invariants.

KW - hyperelliptic curves

KW - quotient curves

KW - etale cohomology

KW - Galois representations

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U2 - 10.1093/qmath/hax053

DO - 10.1093/qmath/hax053

M3 - Article (Academic Journal)

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SP - 747

EP - 768

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 2

ER -

Quotients of hyperelliptic curves and Étale cohomology

Abstract

Keywords

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Arithmetic of hyperelliptic curves.

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Quotients of hyperelliptic curves and Étale cohomology

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

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Arithmetic of hyperelliptic curves.

Cite this