Transcendental Brauer elements via descent on elliptic surfaces

TL;DR

This paper develops a new method to compute transcendental Brauer elements on elliptic surfaces by extending descent techniques, removing previous restrictions related to rational 2-torsion in the Jacobian.

Contribution

It introduces a descent-based approach that generalizes previous methods, enabling the computation of transcendental Brauer elements without assuming rational 2-torsion.

Findings

Provides a new descent method for transcendental Brauer elements

Removes the restriction of rational 2-torsion in Jacobians

Enables broader computation of transcendental classes

Abstract

Transcendental Brauer elements are notoriously difficult to compute. Work of Wittenberg, and later, Ieronymou, gives a method for computing 2-torsion transcendental classes on surfaces that have a genus 1 fibration with rational 2-torsion in the Jacobian fibration. We use ideas from a descent paper of Poonen and Schaefer to remove this assumption on the rational 2-torsion.