论文标题
光谱代数堆栈的Brauer空间
Brauer Spaces of Spectral Algebraic Stacks
论文作者
论文摘要
我们研究了Brauer组是否在光谱代数几何形状中同构的问题。为此，我们证明了带有准蛋白对角线的准混合光谱代数堆叠的扭曲滑轮的紧凑类别，后者接受了准芬特的表现；特别是，我们获得了准搭换滑轮的无界派生类别的紧凑产生，以及存在对此类堆栈的规定支持的紧凑型完美复合物的存在。我们还研究了派生和光谱代数堆栈之间的关系，以便我们的结果可以扩展到派生的代数几何形状的设置。
We study the question of whether the Brauer group is isomorphic to the cohomological one in spectral algebraic geometry. For this, we prove the compact generation of the derived category of twisted sheaves for quasi-compact spectral algebraic stacks with quasi-affine diagonal, which admit a quasi-finite presentation; in particular, we obtain the compact generation of the unbounded derived category of quasi-coherent sheaves and the existence of compact perfect complexes with prescribed support for such stacks. We also study the relationship between derived and spectral algebraic stacks, so that our results can be extended to the setting of derived algebraic geometry.
