This volume contains two related, though independently written, mo- graphs. In Notes on Derived Functors and Grothendieck Duality the ?rst three chapters treat the basics of derived categories and functors, and of the rich formalism, over ringed spaces, of the derived functors, for unbounded com- ? plexes,ofthesheaffunctors?,Hom,f andf wheref isaringed-spacemap. ? Included are some enhancements, for concentrated (i.e., quasi-compact and quasi-separated) schemes, of classical results such as the projection and K.. unneth isomorphisms. The fourth chapter presents the abstract foun- tions of Grothendieck Duality-existence and tor-independent base change for the right adjoint of the derived functor Rf when f is a quasi-proper ? map of concentrated schemes, the twisted inverse image pseudofunctor for separated ?nite-type maps of noetherian schemes, re?nements for maps of ?nite tor-dimension, and a brief discussion of dualizing complexes. In Equivariant Twisted Inverses the theory is extended to the context of diagrams of schemes, and in particular, to schemes with a group-scheme action. An equivariant version of the twisted inverse-image pseudofunctor is de?ned, and equivariant versions of some of its important properties are proved, including Grothendieck duality for proper morphisms, and ?
at base change. Also, equivariant dualizing complexes are dealt with. As an appli- tion,ageneralizedversionofWatanabe'stheoremontheGorensteinproperty of rings of invariants is proved. More detailed overviews are given in the respective Introductions.
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Number of pages: 478
Weight: 753 g
Dimensions: 235 x 155 x 25 mm
Edition: 2009 ed.
From the reviews:
"The appearance of a well-planned, detailed and up-to-date exposition of a topic in abstract algebraic geometry is good news, and the book by J. Lipman and M. Hashimoto definitely has all the above qualities. ... get the book in its current state now than to wait for years until the authors produce a more unified presentation. To conclude, the book by Joseph Lipman and Mitsuyasu Hashimoto is an important contribution to an important task of explaining the main ideas of abstract algebraic geometry ... ." (George Shabat, Bulletin of the London Mathematical Society, March, 2010)