2012/06/13 by Daniel Schäppi, Schäppi, Daniel
Mathematics · #14A20 #16T05 #18D20 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #math.AG #math.AT #math.CT #msc:14A20 #msc:16T05 #msc:18D20
paper · pdf · doi:10.48550/arxiv.1206.2764
64 pages
arxiv created 2012/06/13 · arxiv updated 2012/06/14
Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in this case the category of its finite dimensional representations. Lurie's result that the pseudofunctor which sends a geometric stack to its category of quasi-coherent sheaves is fully faithful provides a conceptual explanation for why this works. In this paper we prove a generalized Tannakian recognition theorem, in order to characterize a part of the image of the extension of the above pseudofunctor to algebraic stacks in the sense of Naumann. This allows us to further investigate a conjecture by Richard Pink about categories of filtered modules, which were defined by Fontaine and Laffaille to construct p-adic Galois representations. In order to do this we give a new characterization of Adams Hopf algebroids, which also allows us to answer a question posed by Mark Hovey.