Author

Alexander Perry

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Preprint Oct 2026

Generalized Bogomolov--Gieseker inequalities via Frobenius

We establish a Bogomolov--Gieseker-type inequality for tilt-semistable objects on smooth projective varieties of dimension $\geq 3$, in the spirit of the Bayer--Macr\`i--Toda conjecture. A key ingredient is an analysis of the action of the Frobenius morphism on tilt-semistable objects. As an application, we prove the C...

Chun-Yi Li, Zhi-Yu Liu, Alexander Perry et al. · 1 citation · ⚡1

Preprint Aug 2026

The period-index conjecture is false for motivic reasons

For any integer $d \geq 3$ and any algebraically closed field $k$ of characteristic $0$ and transcendence degree at least $d-3$, or of characteristic $p>2$ and transcendence degree at least $d-2$, we construct a $d$-dimensional variety over $k$ with a Brauer class of period $2$ and index $2^d$, violating the period-ind...

Alexander Perry · 1 citation