算术曲线上的Gerbe修补和Mayer-Vietoris序列
Gerbe patching and a Mayer-Vietoris sequence over arithmetic curves
摘要：
我们讨论了算术曲线上的格贝的修补技术和局部-全局原则。我们的补丁设置是由Harbater，Hartmann和Krashen介绍的。我们对gerbes的结果可以被看作是他们对torsors的结果的2-范畴类似。在此过程中，我们还讨论了bitorsor修补和bitorsor的局部-全局原则。作为这些结果的应用，我们得到了关于值在交叉模G->Aut（G）中的非交换超上同调集的补片的Mayer-Vietoris序列，其中G是线性代数群.利用Gerbes的局部-整体原理，我们还证明了线性代数群H下特殊（如SL_n和Sp_2 n）的齐性空间上点的局部-整体原理。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
