Foundations of Grothendieck duality for diagrams of schemes / Joseph Lipman, Mitsuyasu Hashimoto

This volume is composed of two related, though independently written, monographs of nearly equal size. The unifying main theme is Grothendieck duality theory, which is then developed in different contexts.

The first part, written by J. Lipman, is titled “Notes on Derived Functors and Grothendieck Duality”. As the author points out, this is an elaborated version of his lecture notes begun in the late 1980s, largely available from his home page since then. These notes were meant to be accessible to mid-level graduate students interested in studying the powerful framework of Grothendieck duality in a profound, systematic and coherent manner. In their present polished form, these notes are organized in four chapters, each of which is divided in several sections. ... In the second part of the book, written by M. Hashimoto and titled “Equivariant Twisted Inverses”, the abstract theory developed in the foregoing introductory notes is extended to the context of diagrams of schemes. ... Altogether, both parts of the book are written in an utmost lucid, comprehensive and detailed style. The first part is largely of introductory nature, though being presented on a highly abstract and advanced level, whereas the second part must be seen as a related and generalizing pure research monograph of topical character. The interested reader will certainly appreciate the wealth of general material on abstract Grothendieck duality provided by this set of lecture notes, and the authors’ expository expertise likewise. (Zentralblatt)