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2016 Arithmetic invariant theory and 2-descent for plane quartic curves
Jack Thorne
Algebra Number Theory 10(7): 1373-1413 (2016). DOI: 10.2140/ant.2016.10.1373

Abstract

Given a smooth plane quartic curve C over a field k of characteristic 0, with Jacobian variety J, and a marked rational point P C(k), we construct a reductive group G and a G-variety X, together with an injection J(k)2J(k)G(k)X(k). We do this using the Mumford theta group of the divisor 2Θ of J, and a construction of Lurie which passes from Heisenberg groups to Lie algebras.

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Jack Thorne. "Arithmetic invariant theory and 2-descent for plane quartic curves." Algebra Number Theory 10 (7) 1373 - 1413, 2016. https://doi.org/10.2140/ant.2016.10.1373

Information

Received: 2 April 2015; Revised: 29 April 2016; Accepted: 18 July 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 06633200
MathSciNet: MR3554236
Digital Object Identifier: 10.2140/ant.2016.10.1373

Subjects:
Primary: 11D25
Secondary: 11E72

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.10 • No. 7 • 2016
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