Gerbe patching and a Mayer-Vietoris sequence over arithmetic curves
Abstract
We discuss patching techniques and local-global principles for gerbes over arithmetic curves. Our patching setup is that introduced by Harbater, Hartmann and Krashen. Our results for gerbes can be viewed as a 2-categorical analogue on their results for torsors. Along the way, we also discuss bitorsor patching and local-global principles for bitorsors. As an application of these results, we obtain a Mayer-Vietoris sequence with respect to patches for non-abelian hypercohomology sets with values in the crossed module G->Aut(G) for G a linear algebraic group. Using local-global principles for gerbes, we also prove local-global principles for points on homogeneous spaces under linear algebraic groups H that are special (e.g. SL_n and Sp_2n) for certain kind of stabilizers.
Keywords
Cite
@article{arxiv.1706.03387,
title = {Gerbe patching and a Mayer-Vietoris sequence over arithmetic curves},
author = {Bastian Haase},
journal= {arXiv preprint arXiv:1706.03387},
year = {2017}
}