**Contemporary Mathematics**

Volume: 244;
2000;
126 pp;
Softcover

MSC: Primary 14;
Secondary 13; 32

**Print ISBN: 978-0-8218-1942-5
Product Code: CONM/244**

List Price: $44.00

AMS Member Price: $35.20

MAA Member Price: $39.60

**Electronic ISBN: 978-0-8218-7834-7
Product Code: CONM/244.E**

List Price: $41.00

AMS Member Price: $32.80

MAA Member Price: $36.90

# Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes

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*Leovigildo Alonso Tarrío; Ana Jeremías López; Joseph Lipman*

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 Grothendieck Duality, unifying
diverse topics. For example, local and global duality appear as different cases
of the same theorem. Even for ordinary schemes, the approach—inspired by that
of Deligne and Verdier—is considerably more general than the one in
Hartshorne's classic ”Residues and Duality.“ Moreover, close attention is paid
to the category-theoretic aspects, especially to justification of all needed
commutativities in diagrams of derived functors.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry.

#### Reviews & Endorsements

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