论文标题
张量类别和方案的纤维产品的本地化
Localizations of tensor categories and fiber products of schemes
论文作者
论文摘要
我们证明，Quasi-Coherent模块的张量类别$ \ MATHSF {QCOH}（X \ TIMES_S Y）$在准连续性准分离方案的纤维产品上是$ \ Mathsf {qCoh}（x）$和$ \ m nathssf（y Mathsf）的bicate-parkorical Puskout $ \ mathsf {qCoh}（s）$在$ 2 $ - 共完成线性张量类别的类别中。特别是，$ \ mathsf {qcoh}（x \ times y）$是$ \ mathsf {qcoh}（x）$和$ \ m athsf {qcoh}（y）$的bicategorical coproduct。为此，我们介绍了偶像，可以将其视为非安装理想，并使用它们来研究共同张量类别的局部定位。
We prove that the tensor category of quasi-coherent modules $\mathsf{Qcoh}(X \times_S Y)$ on a fiber product of quasi-compact quasi-separated schemes is the bicategorical pushout of $\mathsf{Qcoh}(X)$ and $\mathsf{Qcoh}(Y)$ over $\mathsf{Qcoh}(S)$ in the $2$-category of cocomplete linear tensor categories. In particular, $\mathsf{Qcoh}(X \times Y)$ is the bicategorical coproduct of $\mathsf{Qcoh}(X)$ and $\mathsf{Qcoh}(Y)$. For this we introduce idals, which can be seen as non-embedded ideals, and use them to study localizations of cocomplete tensor categories in general.
