Brauer spaces of spectral algebraic stacks

초록

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 in the setting of spectral algebraic stacks. In particular, we obtain the compact generation of the infinity$\infty$-category of quasi-coherent sheaves and the existence of compact perfect complexes with prescribed support for such stacks. We extend these results to derived algebraic geometry by studying the relationship between derived and spectral algebraic stacks.