Formal groups in genus 2. (English) Zbl 0702.14025

For any curve of genus two with a rational Weierstrass point defined over a field of characteristic other \(than\quad 2,\) we find equations defining a projective embedding for its Jacobian, and determine its group law. When the curve is defined over a ring complete under a non-archimedean valuation, this allows us to find explicit parameters for the formal group on the kernel of reduction of the Jacobian modulo the maximal ideal of the ring. The calculations are facilitated by first considering curves defined over the complex numbers and employing theta functions.
Reviewer: D.Grant


14H45 Special algebraic curves and curves of low genus
14K25 Theta functions and abelian varieties
14H40 Jacobians, Prym varieties
14H55 Riemann surfaces; Weierstrass points; gap sequences
14L05 Formal groups, \(p\)-divisible groups
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