Complete Intersections of Two Quadrics and Galois Cohomology

TL;DR

This paper establishes a natural injection linking Galois cohomology of 2-torsion subgroups of Jacobians of hyperelliptic curves to isomorphism classes of nonsingular complete intersections of two quadrics, generalizing prior results.

Contribution

It introduces a new connection between Galois cohomology and geometric classifications of complete intersections, extending Flynn and Skorobogatov's work to arbitrary genus.

Findings

Constructed a natural injection for hyperelliptic curves of any genus.

Generalized previous results to a broader class of curves.

Provides a new framework for understanding the relationship between Galois cohomology and algebraic geometry.

Abstract

For each nonsingular hyperelliptic curve of arbitrary genus, we construct a natural injection from the Galois cohomology of 2-torsion subgroups of Jacobian varieties of the curve to the set of isomorphism classes of nonsingular complete intersections of two quadrics. This gives a generalization of the result of Flynn and Skorobogatov.