论文标题
本地完整的交叉图和代理小型财产
Locally complete intersection maps and the proxy small property
论文作者
论文摘要
事实证明，如果且只有$ s $仅作为bimodule代理，则在本质上是有限的noetherian戒指的地图$φ\ colon r \ to s $ s $ s $是有限类型的，平面是本地完整的交叉点。这意味着由$ s $作为模块产生的厚子类别在包裹的代数$ s \ otimes_rs $上包含一个完美的复合体，该复合体完全支持对角线理想。在经典结果的精神上，$φ$在且仅当$ s $作为双模型时，也就是说，这本身就是相当于完美的复合物。还建立了处理方案之间地图的几何类似物。应用程序包括更简单的分解定理证明，用于局部完整的交叉图。
It is proved that a map $φ\colon R\to S$ of commutative noetherian rings that is essentially of finite type and flat is locally complete intersection if and only $S$ is proxy small as a bimodule. This means that the thick subcategory generated by $S$ as a module over the enveloping algebra $S\otimes_RS$ contains a perfect complex supported fully on the diagonal ideal. This is in the spirit of the classical result that $φ$ is smooth if and only if $S$ is small as a bimodule, that is to say, it is itself equivalent to a perfect complex. The geometric analogue, dealing with maps between schemes, is also established. Applications include simpler proofs of factorization theorems for locally complete intersection maps.
