**Contemporary Mathematics**

Volume: 159;
1994;
444 pp;
Softcover

MSC: Primary 13;
Secondary 14

**Print ISBN: 978-0-8218-5188-3
Product Code: CONM/159**

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

**Electronic ISBN: 978-0-8218-7750-0
Product Code: CONM/159.E**

List Price: $78.00

AMS Member Price: $62.40

MAA Member Price: $70.20

# Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra

Share this page *Edited by *
*William J. Heinzer; Craig L. Huneke; Judith D. Sally*

This volume contains refereed papers on themes explored at the AMS-IMS-SIAM Summer Research Conference, Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, held at Mount Holyoke College in 1992. The conference featured a series of one-hour invited lectures on recent advances in commutative algebra and interactions with such areas as algebraic geometry, representation theory, and combinatorics. The major themes of the conference were tight closure Hilbert functions, birational algebra, free resolutions and the homological conjectures, Rees algebras, and local cohomology. With contributions by several leading experts in the field, this volume provides an excellent survey of current research in commutative algebra.

#### Readership

Mathematicians interested in commutative algebra and its applications.

# Table of Contents

## Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra

- Contents v6 free
- Preface vii8 free
- Grothendieck"s localization problem 110 free
- A simple proof of Grothendieck's theorem on the parafactoriality of local rings 1524
- Resolutions with a given Hilbert function 1928
- Complete ideals in algebra and geometry 2736
- On the Cohen-Macaulay type of perfect ideals 4150
- On the Gorensteinness of graded rings associated to ideals of analytic deviation one 5160
- Prime ideals in birational extensions of polynomial rings 7382
- On the index of a homogeneous Gorenstein ring 95104
- Solid closure 103112
- 1. Introduction 104113
- 2. Solid modules and solid algebras 107116
- 3. Formally solid modules and algebras 114123
- 4. Generic forcing algebras 118127
- 5. Solid closure 120129
- 6. Minimal solid algebras 128137
- 7. S-regular rings 130139
- 8. Comparison with tight closure in characteristic p 139148
- 9. A formal power series criterion 145154
- 10. Shadow homology 147156
- 11. Big Cohen-Macaulay algebras and tight closure in equal characteristic zero 153162
- 12. The case of dimension two 160169
- 13. Regular rings revisited 164173
- 14. Questions 168177

- Tight closure in equal characteristic, big Cohen-Macaulay algebras, and solid closure 173182
- Indecomposable canonical modules and connectedness 197206
- Multiplicities in graded rings I: The general theory 209218
- Pfaffian identities, with applications to free resolutions, DG-algebras, and algebras with straightening law 269278
- Proximity inequalities for complete ideals in two-dimensional regular local rings 293302
- Cohomological annihilators and Castelnuovo-Mumford regularity 307316
- Local-global principle for annihilation of local cohomology 329338
- Multiplicities and Chern classes 333342
- A computation of local cohomology 351360
- Algebra structures for graded free resolutions 357366
- Primary decompositions of powers of ideals 367376
- Artin-Nagata properties and reductions of ideals 373382
- Hilbert functions, analytic spread, and Koszul homology 401410
- Infinite cyclic covers of strongly F-regular rings 423432
- Torsion in Picard groups of affine rings 433442