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Commutative Algebra and Noncommutative Algebraic Geometry

Volume 1. Expository Articles

£141.00

Part of Mathematical Sciences Research Institute Publications

Editors:
David Eisenbud, University of California, Berkeley
Srikanth B. Iyengar, University of Utah
Anurag K. Singh, University of Utah
J. Toby Stafford, University of Manchester
Michel Van den Bergh, Fonds Wetenschappelijk Onderzoek , Belgium

David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford, Michel Van den Bergh, Jason P. Bell, Christine Berkesch, Frank-Olaf Schreyer, Holger Brenner, Maria Chlouveraki, Steven Dale Cutkosky, Craig Huneke, Claudiu Raicu, Matilde Marcolli, Gonçalo Tabuada, Jason McCullough, Irena Peeva, Anne V. Shepler, Sarah Witherspoon, Karen E. Smith, Wenliang Zhang, Duco van Straten, Michaela Vancliff, Uli Walther, Anton Leykin, Amnon Yekutieli

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Date Published: November 2015
availability: Available
format: Hardback
isbn: 9781107065628

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Description

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Courses

About the Authors

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.
- High-quality articles survey the current state of knowledge in this extremely active field
- Focuses on areas of common interest which emphasise the lively interaction between commutative algebra and noncommutative algebraic geometry
- Valuable to researchers and graduate students studying algebra and algebraic geometry
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Product details
- Date Published: November 2015
- format: Hardback
- isbn: 9781107065628
- length: 462 pages
- dimensions: 234 x 156 x 25 mm
- weight: 0.82kg
- contains: 15 b/w illus. 50 exercises
- availability: Available
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 Gonçalo Tabuada
7. Infinite graded free resolutions Jason McCullough and Irena Peeva
8. Poincaré–Birkhoff–Witt theorems Anne V. Shepler and Sarah Witherspoon
9. Frobenius splitting in commutative algebra Karen E. Smith and Wenliang Zhang
10. From Briançon–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.
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Editors
David Eisenbud, University of California, Berkeley
David Eisenbud is a Professor in the Department of Mathematics at the University of California, Berkeley.
Srikanth B. Iyengar, University of Utah
Srikanth B. Iyengar is a Professor in the Department of Mathematics at the University of Utah.
Anurag K. Singh, University of Utah
Anurag K. Singh is a Professor in the Department of Mathematics at the University of Utah.
J. Toby Stafford, University of Manchester
J. Toby Stafford is Professor in the Department of Mathematics at the University of Manchester.
Michel Van den Bergh, Fonds Wetenschappelijk Onderzoek , Belgium
Michel Van den Bergh is Director of Research at the Research Foundation - Flanders (FWO), Belgium.
Series editor Cam Learning use ONLY
Mathematical Sciences Research Institute
Contributors
David Eisenbud, Srikanth B. Iyengar, Anurag K. Singh, J. Toby Stafford, Michel Van den Bergh, Jason P. Bell, Christine Berkesch, Frank-Olaf Schreyer, Holger Brenner, Maria Chlouveraki, Steven Dale Cutkosky, Craig Huneke, Claudiu Raicu, Matilde Marcolli, Gonçalo Tabuada, Jason McCullough, Irena Peeva, Anne V. Shepler, Sarah Witherspoon, Karen E. Smith, Wenliang Zhang, Duco van Straten, Michaela Vancliff, Uli Walther, Anton Leykin, Amnon Yekutieli