Foundations of Grothendieck Duality for Diagrams of Schemes
Foundations of Grothendieck Duality for Diagrams of Schemes
复制标题
DOI：
10.1007/978-3-540-85420-3
复制
发表时间：
2009-02
期刊：
影响因子：
--
通讯作者：
J. Lipman;M. Hashimoto
中科院分区：
文献类型：
--
作者：
J. Lipman;M. Hashimoto
约瑟夫·利普曼：关于派生函子和Grothendieck对偶的注记。-派生范畴和三角范畴。-派生函子。-派生正像和逆像。-方案的抽象Grothendieck对偶。-桥本光裕：等变扭曲逆。-由一对伪函子构成的图的交换性。-环状中心上的SHeaves。-环状中心上SHeaves的派生范畴和派生函子。-S图式上的派生范畴和派生函子。-左和右归纳以及正反像。-通过结构数据对SHeaves的运算。-方案图上的准相干SHeaves。-环状中心上SHeaves的派生函数方案图上模群上的函子。-单纯对象。-下降理论。-局部Notherian性质。-方案群。-Bökstedt-Neeman分解和HyperExt Sheaves。-派生的直接映象函子的右伴随。-局部外延函子的比较。-两个几乎-伪函子的合成。-图的态射的派生直接映象函子的右伴随。-带限制的扭曲逆的交换性。-开浸没基变。-有序有限范畴上方案图的压缩和合成数据的存在性。-平坦基变化。拟凝聚上同调-与导出的直接映象相容-与导出的右诱导相容-等变的Grothendieck对偶-有限平坦维度的态射-笛卡尔有限态射-笛卡尔正则嵌入和笛卡尔光滑态射-有限类型的群方案平坦-与导出的G-不变性相容-等变对偶化复形和正则模-渡边定理的推广-模图的其他例子
Joseph Lipman: Notes on Derived Functors and Grothendieck Duality.-Derived and Triangulated Categories.-Derived Functors.-Derived Direct and Inverse Image.-Abstract Grothendieck Duality for Schemes.-Mitsuyasu Hashimoto: Equivariant Twisted Inverses.-Commutativity of Diagrams Constructed from a Monoidal Pair of Pseudofunctors.-Sheaves on Ringed Sites.-Derived Categories and Derived Functors of Sheaves on Ringed Sites.-Sheaves over a Diagram of S-Schemes.-The Left and Right Inductions and the Direct and Inverse Images.-Operations on Sheaves Via the Structure Data.-Quasi-Coherent Sheaves Over a Diagram of Schemes.-Derived Functors of Functors on Sheaves of Modules Over Diagrams of Schemes.-Simplicial Objects.-Descent Theory.-Local Noetherian Property.-Groupoid of Schemes.-Bökstedt-Neeman Resolutions and HyperExt Sheaves.-The Right Adjoint of the Derived Direct Image Functor.-Comparison of Local Ext Sheaves.-The Composition of Two Almost-Pseudofunctors.-The Right Adjoint of the Derived Direct Image Functor of a Morphism of Diagrams.-Commutativity of Twisted Inverse with Restrictions.-Open Immersion Base Change.-The Existence of Compactification and Composition Data for Diagrams of Schemes Over an Ordered Finite Category.-Flat Base Change.-Preservation of Quasi-Coherent Cohomology.-Compatibility with Derived Direct Images.-Compatibility with Derived Right Inductions.-Equivariant Grothendieck's Duality.-Morphisms of Finite Flat Dimension.-Cartesian Finite Morphisms.-Cartesian Regular Embeddings and Cartesian Smooth Morphisms.-Group Schemes Flat of Finite Type.-Compatibility with Derived G-Invariance.-Equivariant Dualizing Complexes and Canonical Modules.-A Generalization of Watanabe's Theorem.-Other Examples of Diagrams of Schemes.