Studies in duality on noetherian formal schemes and non-noetherian ordinary schemes / Leovigildo Alonso Tarrío, Ana Jeremías López, Joseph Lipman.

Format:

Book

Author/Creator:

Alonso Tarrío, Leovigildo, 1962- author.

Jeremías López, Ana, 1962- author.

Lipman, Joseph, author.

Series:

Contemporary mathematics (American Mathematical Society) ; v. 244.

Contemporary mathematics, 0271-4132 ; 244

Language:

English

Subjects (All):

Duality theory (Mathematics).

Schemes (Algebraic geometry).

Physical Description:

1 online resource (138 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1999]

Language Note:

English

Summary:

This volume contains three papers on the foundations of Grothendieck duality on Noetherian formal schemes and on not-necessarily-Noetherian ordinary schemes. The first paper presents a self-contained treatment for formal schemes which synthesizes several duality-related 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 Greenlees-May 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 pseudo-coherence of complexes under proper pseudo-coherent maps. This work gives a detailed introduction to the subject of Grothendieck Duality. The approach is unique in its presentation of a complex series of special cases that build up to the main results.

Contents:

""Contents""; ""Preface""; ""Part 1: Duality and Flat Base Change on Formal Schemes""; ""Part 2: Greenlees-May Duality on Formal Schemes""; ""Part 3: Non-noetherian Grothendieck Duality""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""K""; ""L""; ""R""; ""S""; ""T""; ""V""; ""W""; ""Y""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-8218-7834-4

0-8218-5580-8