Grothendieck拓扑与理想闭包运算
Grothendieck topologies and ideal closure operations
摘要：
我们将理想和子模的闭包运算与非平坦Grothendieck拓扑联系起来。我们展示了如何Grothendieck拓扑上的仿射计划诱导一个闭包运算在一个自然的方式，以及如何构建一个给定的闭包运算满足某些性质的Grothendieck拓扑，诱导此操作。这样，我们涉及到根的满射拓扑和构造拓扑，整闭包的淹没拓扑，适当的拓扑和Voevodsky的h-拓扑，Frobenius封闭的Frobenius拓扑和加上封闭的有限拓扑。由Zapriki滤子诱导的拓扑产生闭包运算，这些运算在遗传挠理论的名义下进行研究。Grothendieck拓扑通过提供上同调理论、整体瓣环、正合性和茎的概念丰富了相应的闭包运算。
英文摘要：
We relate closure operations for ideals and for submodules to non-flat Grothendieck topologies. We show how a Grothendieck topology on an affine scheme induces a closure operation in a natural way, and how to construct for a given closure operation fulfilling certain properties a Grothendieck topology which induces this operation. In this way we relate the radical to the surjective topology and the constructible topology, the integral closure to the submersive topology, to the proper topology and to Voevodsky's h-topology, the Frobenius closure to the Frobenius topology and the plus closure to the finite topology. The topologies which are induced by a Zariski filter yield the closure operations which are studied under the name of hereditary torsion theories. The Grothendieck topologies enrich the corresponding closure operation by providing cohomology theories, rings of global sections, concepts of exactness and of stalks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
