Foundations of Grothendieck duality for diagrams of schemes

The first part 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 Künneth isomorphisms. In the second part, 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. INDICE: From the contents 1. Derived and Triangulated Categories.- 2. Derived Functors.- 3. Derived Direct and Inverse Image.- 4. Abstract Grothendieck Duality for schemes.- 1. Commutativity of diagrams constructed from a monoidalpair of pseudofunctors.- 2. Sheaves on ringed sites.- 3. Derived categories and derived functors of sheaves on ringed sites.- 4. Sheaves over a diagram of S-schemes.- 5. The left and right inductions and the direct and inverse images.- 6. Operations on sheaves via the structure data.- 7. Quasi-coherent sheavesover a diagram of schemes.- 8. Derived functors of functors on sheaves of modules over diagrams of schemes.- 9. Simplicial objects.- 10. Descent theory.- 11. Local noetherian property.- 12. Groupoid of schemes.- 13. Boekstedt-Neeman resolutions and hyperExt sheaves.- 14. The right adjoint of the derived directimage functor.- 15. Comparison of local Ext sheaves.- 16. The Composition of two almost-pseudofunctors.

• ISBN: 978-3-540-85419-7
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 460
• Fecha Publicación: 01/01/2009
• Nº Volúmenes: 1
• Idioma: Inglés