Commutative algebra and noncommutative algebraic geometry

Author(s)

• Eisenbud, David
• Iyengar, Srikanth
• Singh, Anurag K.
• Stafford, J. T.
• Bergh, M. van den

Bibliographic Information

Commutative algebra and noncommutative algebraic geometry

edited by David Eisenbud ... [et al.]

（Mathematical Sciences Research Institute publications, 67-68）

Cambridge University Press, 2015

• v. 1 : hardback
• v. 2 : hardback

Note

Other editors: Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford, Michel Van den Bergh

v. 1: Expository articles

v. 2: Research articles

Includes bibliographical references

Description and Table of Contents

Volume

v. 1 : hardback ISBN 9781107065628

Description

In the 2012-13 academic year, the Mathematical Sciences Research Institute, Berkeley, hosted programs in Commutative Algebra (Fall 2012 and Spring 2013) and Noncommutative Algebraic Geometry and Representation Theory (Spring 2013). There have been many significant developments in these fields in recent years; what is more, the boundary between them has become increasingly blurred. This was apparent during the MSRI program, where there were a number of joint seminars on subjects of common interest: birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, and tilting theory, to name a few. These volumes reflect the lively interaction between the subjects witnessed at MSRI. The Introductory Workshops and Connections for Women Workshops for the two programs included lecture series by experts in the field. The volumes include a number of survey articles based on these lectures, along with expository articles and research papers by participants of the programs. Volume 1 contains expository papers ideal for those entering the field.

Table of Contents

• Preface David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford and Michel Van den Bergh
• 1. Growth functions Jason P. Bell
• Syzygies, finite length modules, and random curves Christine Berkesch and Frank-Olaf Schreyer
• 2. Vector bundles and ideal closure operations Holger Brenner
• 3. Hecke algebras and symplectic reflection algebras Maria Chlouveraki
• 4. Limits in commutative algebra and algebraic geometry Steven Dale Cutkosky
• 5. Introduction to uniformity in commutative algebra Craig Huneke and Claudiu Raicu
• 6. Noncommutative motives and their applications Matilde Marcolli and Goncalo Tabuada
• 7. Infinite graded free resolutions Jason McCullough and Irena Peeva
• 8. Poincare-Birkhoff-Witt theorems Anne V. Shepler and Sarah Witherspoon
• 9. Frobenius splitting in commutative algebra Karen E. Smith and Wenliang Zhang
• 10. From Briancon-Skoda to Scherk-Varchenko Duco van Straten
• 11. The interplay of algebra and geometry in the setting of regular algebras Michaela Vancliff
• 12. Survey on the D-module f s Uli Walther, with an appendix by Anton Leykin
• 13. Introduction to derived categories Amnon Yekutieli.

Volume

v. 2 : hardback ISBN 9781107149724

Description

In the 2012-13 academic year, the Mathematical Sciences Research Institute, Berkeley, hosted programs in Commutative Algebra (Fall 2012 and Spring 2013) and Noncommutative Algebraic Geometry and Representation Theory (Spring 2013). There have been many significant developments in these fields in recent years; what is more, the boundary between them has become increasingly blurred. This was apparent during the MSRI program, where there were a number of joint seminars on subjects of common interest: birational geometry, D-modules, invariant theory, matrix factorizations, noncommutative resolutions, singularity categories, support varieties, and tilting theory, to name a few. These volumes reflect the lively interaction between the subjects witnessed at MSRI. The Introductory Workshops and Connections for Women Workshops for the two programs included lecture series by experts in the field. The volumes include a number of survey articles based on these lectures, along with expository articles and research papers by participants of the programs. Volume 2 focuses on the most recent research.

Table of Contents

• Preface David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford and Michel Van den Bergh
• 1. When is a squarefree monomial ideal of linear type? Ali Alilooee and Sara Faridi
• 2. Modules for elementary abelian groups and hypersurface singularities David J. Benson
• 3. Ideals generated by superstandard tableaux Andrew Berget, Winfried Bruns and Aldo Conca
• 4. Zariski topologies on stratified spectra of quantum algebras Kenneth A. Brown and Kenneth R. Goodearl
• 5. The derived category of a graded Gorenstein ring Jesse Burke and Greg Stevenson
• 6. Singularities with respect to Mather-Jacobian discrepancies Lawrence Ein and Shihoko Ishii
• 7. Reduction numbers and balanced ideals Louiza Fouli
• 8. Unipotent and Nakayama automorphisms of quantum nilpotent algebras Kenneth R. Goodearl and Milen T. Yakilmov
• 9. Formal fibers of prime ideals in polynomial rings William Heinzer, Christel Rotthaus and Sylvia Wiegand
• 10. Bounding the socles of powers of squarefree monomial ideals Jurgen Herzog and Takayuki Hibi
• 11. An intriguing ring structure on the set of d-forms Jurgen Herzog, Leila Sharifan and Matteo Varbaro
• 12. On the subadditivity problem for maximal shifts in free resolutions Jurgen Herzog and Hema Srinivasan
• 13. The cone of Betti tables over a rational normal curve Manoj Kummini and Steven V. Sam
• 14. Adjoint associativity - an invitation to algebra in -categories Joseph Lipman.

by "Nielsen BookData"

Details

• NCID: BB20320774
• ISBN:
  • 9781107065628
  • 9781107149724
• LCCN: 2015044937
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York, N.Y.
• Pages/Volumes: 2 v.
• Size: 25 cm
• Classification:
  • LCC : QA251.3
  • DC23 : 512/.44
• Subject Headings:
  • LCSH : Commutative algebra
  • LCSH : Geometry, Algebraic
• Parent Bibliography ID:
  • BA00044859