TY  - BOOK
AU  - Lipman,Joseph
AU  - Hashimoto, Mitsuyasu
TI  - Foundations of Grothendieck duality for diagrams of schemes
SN  - 9783540854197
U1  - 515.7 
PY  - 2009///
CY  - Berlin
PB  - Springer-Verlag
KW  - Categories (Mathematics)
KW  - Duality theory (Mathematics)
KW  - Functor theory
KW  - Schemes (Algebraic geometry)
KW  - Sheaf theory
N1  - 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 Kttnneth 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
ER  -