The derived Picard group of an affine Azumaya algebra
The derived Picard group of an affine Azumaya algebra
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DOI：
10.1007/s00029-016-0249-7
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发表时间：
2016-01
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影响因子：
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通讯作者：
C. Negron
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文献类型：
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作者：
C. Negron
本文描述了Azumaya代数A在仿射概型上的导出Picard群，X上整数的常数层的整体截面的Xin项，X的Picard群以及A的Brauer类在的作用下的稳定子.特别地，我们发现Azumaya代数的导出Picard群一般不同构于其基础方案。在平凡Azumaya代数的情况下，我们的结果改进了Yekutieli对交换代数的导出Picard群的描述。我们还得到，作为一个推论，一个替代的证明结果的Antieau的关系导出等价的Brauer等价的仿射Azumaya代数。对有限特征的外尔代数的例子进行了较为详细的研究。
We describe the derived Picard group of an Azumaya algebraAon an affine schemeXin terms of global sections of the constant sheaf of integers onX, the Picard group ofX, and the stabilizer of the Brauer class ofAunder the action of. In particular, we find that the derived Picard group of an Azumaya algebra is generally not isomorphic to that of the underlying scheme. In the case of the trivial Azumaya algebra, our result refines Yekutieli’s description of the derived Picard group of a commutative algebra. We also get, as a corollary, an alternate proof of a result of Antieau which relates derived equivalences to Brauer equivalences for affine Azumaya algebras. The example of a Weyl algebra in finite characteristic is examined in some detail.