Abstract
Using formal-local methods, we prove that a separated and normal tame Artin surface has the resolution property. By proving that normal tame Artin stacks can be rigidified, we ultimately reduce our analysis to establishing the existence of Azumaya algebras. Our construction passes through the case of tame Artin gerbes, tame Artin curves, and algebraic space surfaces, each of which we establish independently.
Funding statement: A part of this research was conducted in the framework of the research training group GRK 2240: Algebro-geometric Methods in Algebra, Arithmetic and Topology, which is funded by the DFG.
Acknowledgements
A large part of this paper comes from the authors Ph.D thesis. I would like to thank my advisor, Max Lieblich, for his generous support and guidance. I am also indebted to Jarod Alper and Aise Johan de Jong for their encouragement and suggestions. I also benefited from helpful discussions with Dan Abramovich, Dan Edidin, Lucas Braune, Jack Hall, Ariyan Javanpeykar, Andrew Kresch, Minseon Shin, David Rydh, Stefan Schröer, Jason Starr, and Angelo Vistoli. I would also like to thank the referee for carefully reading an earlier version of this paper and providing many helpful comments.
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