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Andrew Kresch

Publications and source records attributed to Andrew Kresch.

At least 19 recordsLinked to original sources
arXiv2025

Intermediate Jacobians and Burnside invariants

We propose new invariants in equivariant birational geometry, combining equivariant intermediate Jacobians and the Burnside formalism, for smooth rationally connected threefolds with actions of finite groups.

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arXiv2025

Equivariant unirationality of toric varieties

We introduce a torsor-theoretic obstruction to equivariant unirationality and show that it is also sufficient for actions of finite groups on toric varieties arising from automorphisms of the torus.

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arXiv2023

Formal GAGA for gerbes

Fix an $I$-adically complete Noetherian ring $A$ and suppose $X$ is a proper $A$-scheme. This article concerns the relationship between the Brauer group of $X$ and that of the various $X_n$ where $X_n$ is the fiber over $A/I^{n+1}$. In particular, we answer a question of Grothendieck by showing that, in positive and mixed characteristic, there are examples of $X$ with nontrivial Brauer classes that restrict to zero on all the $X_n$. We characterize such behavior, prove this cannot happen in characteristic zero, and deduce a formal GAGA statement for Brauer classes.

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arXiv2022

Cohomology of finite subgroups of the plane Cremona group

An equivariant stable birational invariant of an action of a finite group on a smooth projective variety is the first cohomology group of the Picard module. Bogomolov-Prokhorov and Shinder computed this for actions of cyclic groups on rational surfaces, with maximal stabilizers, in terms of the geometry of the fixed point locus. Using the Brauer group of the quotient stack, we extend the computation to more general actions and relate it to the equivariant Burnside group formalism.

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arXiv2020

Equivariant birational types and Burnside volume

We introduce equivariant Burnside groups, new invariants in equivariant birational geometry, generalizing birational symbols groups for actions of finite abelian groups, due to Kontsevich, Pestun, and the second author, and study their properties. We establish a specialization map for the equivariant birational type of a smooth algebraic variety with an action of a finite group.

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arXiv2019

Birational types of algebraic orbifolds

We introduce a variant of the birational symbols group of Kontsevich, Pestun, and the second author, and use this to define birational invariants of algebraic orbifolds.

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