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math.AG2025
The étale local structure of algebraic stacks
Jarod Alper, Jack Hall, David Rydh
We prove that an algebraic stack with affine stabilizers over an arbitrary base is étale-locally a quotient stack around any point with a linearly reductive stabilizer. This gener…
math.AG2025
Unipotent morphisms
Daniel Bragg, Jack Hall, Siddharth Mathur
We introduce the theory of unipotent morphisms of algebraic stacks and prove a surprising local to global principle for a class of vector bundles. Two sample applications of our me…
math.AG2024
A generalized Bondal-Orlov full faithfulness criterion for Deligne-Mumford stacks
Jack Hall, Kyle Priver
Let , be smooth projective varieties over . Let be a bounded complex of coherent sheaves on and let $Φ_K \colon \mathsf{D}^b_{\mathsf{Coh}}(X) \…