The period-index problem for complex tori
James Hotchkiss
TL;DR
This paper solves the period-index problem for the Brauer group of general complex tori of dimension three or more, providing explicit formulas and showing the conjecture fails in this setting.
Contribution
It provides an explicit formula for the index of Brauer classes on complex tori and demonstrates the failure of the period-index conjecture in this context.
Findings
Explicit formula for the index of Brauer classes on complex tori
Counterexamples to the period-index conjecture in complex-analytic setting
Failure of the conjecture for infinitely many classes on general complex tori of dimension ≥3
Abstract
We solve the period-index problem for the Brauer group of a general complex torus of dimension at least three, giving an explicit formula for the index of each Brauer class. As a consequence, the complex-analytic version of the period-index conjecture is false for infinitely many Brauer classes on a general complex torus of dimension at least three.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models