Vol. 10, No. 7, 2016

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Arithmetic invariant theory and 2-descent for plane quartic curves

Jack A. Thorne

Appendix: Tasho Kaletha

Vol. 10 (2016), No. 7, 1373–1413

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.

arithmetic geometry, descent, invariant theory
Mathematical Subject Classification 2010
Primary: 11D25
Secondary: 11E72
Received: 2 April 2015
Revised: 29 April 2016
Accepted: 18 July 2016
Published: 27 September 2016
Jack A. Thorne
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Wilberforce Road
Cambridge CB3 0WB
United Kingdom
Tasho Kaletha
Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor, MI 48109-1043
United States