Arithmetic invariant theory and 2-descent for plane quartic curves

2016/07/29 by Thorne, Jack A.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1607.08816

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.

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