algebraic geometry

Daniel Litt @littmath · 15h
To my taste this is the best counterexample of the year so far.

[quoted arxiv abstract card]
Title: The period-index conjecture is false
Authors: Alexander Perry
Categories: math.AG
Comments: 17 pages
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  For any uncountable algebraically closed field $k$ of characteristic $0$ and any $d \geq 3$, we construct a variety over $k$ of dimension $d$ with a Brauer class which violates the period-index conjecture for Hodge-theoretic reasons. When $d = 3$, our construction works even without the assumption that $k$ is uncountable; in particular, the period-index conjecture fails over $\overline{\mathbf{Q}}$.

mathematicsalgebraic geometryarxiv