Arithmetic invariant theory and 2-descent for plane quartic curves
Number Theory
2016-08-01 v1
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 of 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 J, and a construction of Lurie which passes from Heisenberg groups to Lie algebras.
Cite
@article{arxiv.1607.08816,
title = {Arithmetic invariant theory and 2-descent for plane quartic curves},
author = {Jack A. Thorne},
journal= {arXiv preprint arXiv:1607.08816},
year = {2016}
}
Comments
With an appendix by Tasho Kaletha. This paper will appear in Algebra & Number Theory