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Further remarks on derived categories of algebraic stacks (2205.09312v1)

Published 19 May 2022 in math.AG

Abstract: Let $X$ be an algebraic stack with quasi-affine diagonal of finite type over a field $k$ of characteristic $0$. We extend the well-known equivalence $\mathsf{D}+(\mathsf{QCoh}(X)) \simeq \mathsf{D}{\mathrm{qc}}+(X)$ to unbounded derived categories. We also prove that if $X$ is smooth over $k$, then $\mathsf{D}{\mathrm{qc}}(X)$ is compactly generated. We accomplish the former using the descendable algebras of Mathew. We also establish related results in positive and mixed characteristics.

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