论文标题
关于代数堆栈的派生类别的进一步评论
Further remarks on derived categories of algebraic stacks
论文作者
论文摘要
让$ x $成为一个代数堆栈，具有有限型类型的准对角线，而特征$ 0 $ $ k $。我们扩展了众所周知的等价$ \ Mathsf {d}^+（\ Mathsf {qCoh}（x））\ simeq \ simeq \ mathsf {d} _ {\ Mathrm {qc}}}}^+（x）$（x）$（x）$到没有结合的派生类别。我们还证明，如果$ x $在$ k $上平稳，则$ \ mathsf {d} _ {\ mathrm {qc}}}}（x）$是紧凑的。我们使用Mathew的后代代数来完成前者。我们还以积极和混合特征建立了相关的结果。
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.
