Foundations of Grothendieck Duality for Diagrams of Schemes (eBook)

Joseph Lipman, Mitsuyasu Hashimoto (Autoren)

eBook Download: PDF

2009 | 2009
X, 478 Seiten
Springer Berlin (Verlag)
978-3-540-85420-3 (ISBN)

Infos

Part One of this book covers the abstract foundations of Grothendieck duality theory for schemes in part with noetherian hypotheses and with some refinements for maps of finite tor-dimension. Part Two extends the theory to the context of diagrams of schemes.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 7.3.2009
• Reihe/Serie: Lecture Notes in Mathematics
• Verlagsort: Berlin
• Sprache: englisch
• Schlagworte: 14A20, 18E30, 14F99, 18A99, 18F99, 14L30 • cohomology • derived functors • diagram of schemes • Grothendieck duality • twisted inverse-image
• ISBN-10: 3-540-85420-7 / 3540854207
• ISBN-13: 978-3-540-85420-3 / 9783540854203