Contemporary Mathematics 2000; 126 pp; softcover Volume: 244 ISBN10: 0821819429 ISBN13: 9780821819425 List Price: US$41 Member Price: US$32.80 Order Code: CONM/244
 This volume contains three papers on the foundations of Grothendieck duality on Noetherian formal schemes and on notnecessarilyNoetherian ordinary schemes. The first paper presents a selfcontained treatment for formal schemes which synthesizes several dualityrelated topics, such as local duality, formal duality, residue theorems, dualizing complexes, etc. Included is an exposition of properties of torsion sheaves and of limits of coherent sheaves. A second paper extends GreenleesMay duality to complexes on formal schemes. This theorem has important applications to Grothendieck duality. The third paper outlines methods for eliminating the Noetherian hypotheses. A basic role is played by Kiehl's theorem affirming conservation of pseudocoherence of complexes under proper pseudocoherent maps. This work gives a detailed introduction to Grothendieck Duality, unifying diverse topics. For example, local and global duality appear as different cases of the same theorem. Even for ordinary schemes, the approachinspired by that of Deligne and Verdieris considerably more general than the one in Hartshorne's classic "Residues and Duality." Moreover, close attention is paid to the categorytheoretic aspects, especially to justification of all needed commutativities in diagrams of derived functors. Readership Graduate students and research mathematicians interested in algebraic geometry. Reviews "This volume consists of three essentially independent articles which are, however, connected by the common theme of duality theory. They provide very interesting treatments of various fundamental aspects of abstract duality theory in the style of Grothendieck for formal and ordinary schemes."  Mathematical Reviews Table of Contents Part 1  L. Alonso, A. Jeremías, and J. Lipman  Duality and flat base change on formal schemes
Part 2  L. Alonso, A. Jeremías, and J. Lipman  GreenleesMay duality on formal schemes
Part 3  J. Lipman  Nonnoetherian Grothendieck duality
 Index
