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Unipotent Morphism Mathematics Pure mathematics Algebraic number FLAGS register Torsion (gastropod) Algebra over a field Discrete mathematics Mathematical analysis Computer science Operating system Medicine Surgery

Daniel Bragg , Jack Hall , Siddharth Mathur ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2110.15041 · OA: W3209227832

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 methods are the following: (1) a unipotent analogue of Gabber's Theorem for torsion $\mathbf{G}_m$-gerbes and (2) smooth Deligne-Mumford stacks with quasi-projective coarse spaces satisfy the resolution property in positive characteristic. Our main tool is a descent result for flags, which we prove using results of Schäppi.