Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field

Eugene Victor Flynna1*

a1 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.

Abstract

An embedding of the Jacobian variety of a curve S0305004100068729_inline1 of genus 2 is given, together with an explicit set of defining equations. A pair of local parameters is chosen, for which the induced formal group is defined over the same ring as the coefficients of S0305004100068729_inline1. It is not assumed that S0305004100068729_inline1 has a rational Weierstrass point, and the theory presented applies over an arbitrary ground field (of characteristic ╪ 2, 3, or 5).

(Received July 25 1989)

Footnotes

* Current address: Department of Pure Mathematics and Mathematical Statistics, Cambridge CB2 1SB.