Foundations of Grothendieck Duality for Diagrams of Schemes (Lecture Notes in Mathematics) pdf epub mobi txt 电子书 下载 2026
- 数学
- grothendieck
- 数学-专
- Math
- Grothendieck duality
- Diagrams of schemes
- Algebraic geometry
- Homological algebra
- Category theory
- Derived categories
- Lecture notes
- Mathematics
- Scheme theory
- Cohomology
具体描述
The first part by Joseph Lipman is a full exposition of the abstract foundations of Grothendieck duality theory for schemes (twisted inverse image, tor-independent base change, ...), in part without noetherian hypotheses, and with some refinements for maps of finite tor-dimension. The ground is prepared by a lengthy treatment of the rich formalism of relations among the derived functors, for unbounded complexes over ringed spaces, of the sheaf functors tensor, hom, direct and inverse image. Included are enhancements, for quasi-compact quasi-separated schemes, of classical results such as the projection and K nneth isomorphisms. In the second part, written independantly by Mitsuyasu Hashimoto, the theory is extended to the context of diagrams of schemes. This includes, as a special case, an equivariant theory for schemes with group actions. In particular, after various basic operations on sheaves such as (derived) direct images and inverse images are set up, Grothendieck duality and flat base change for diagrams of schemes are proved. Also, dualizing complexes are studied in this context. As an application to group actions, we generalize Watanabe's theorem on the Gorenstein property of invariant subrings.
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格罗滕迪克的六个算子（张量，hom，推前和拖回），其中最关键的是twisted inverse image functor是（Serre’s duality的推广）性质：局部化，拟函子性，对偶性，本质性质是平坦基互容和构造拟凝聚上同调。凝聚层是向量丛等价物的阿贝范畴。
评分格罗滕迪克的六个算子（张量，hom，推前和拖回），其中最关键的是twisted inverse image functor是（Serre’s duality的推广）性质：局部化，拟函子性，对偶性，本质性质是平坦基互容和构造拟凝聚上同调。凝聚层是向量丛等价物的阿贝范畴。
评分格罗滕迪克的六个算子（张量，hom，推前和拖回），其中最关键的是twisted inverse image functor是（Serre’s duality的推广）性质：局部化，拟函子性，对偶性，本质性质是平坦基互容和构造拟凝聚上同调。凝聚层是向量丛等价物的阿贝范畴。
评分格罗滕迪克的六个算子（张量，hom，推前和拖回），其中最关键的是twisted inverse image functor是（Serre’s duality的推广）性质：局部化，拟函子性，对偶性，本质性质是平坦基互容和构造拟凝聚上同调。凝聚层是向量丛等价物的阿贝范畴。
评分格罗滕迪克的六个算子（张量，hom，推前和拖回），其中最关键的是twisted inverse image functor是（Serre’s duality的推广）性质：局部化，拟函子性，对偶性，本质性质是平坦基互容和构造拟凝聚上同调。凝聚层是向量丛等价物的阿贝范畴。
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