## Abstract

A finitely generated module * C * over a noetherian ring * R * is semidualizing if Hom _{ R } ( * C * , * C * )≅ * R * and Ext ^{ i } _{ R } ( * C * , * C * )=0 for all * i * ≥1. These modules arise in several contexts, for instance, in the study of divisors, in the study of local ring homomorphisms, and in representation theory. In 1974 Vasconcelos conjectured that a Cohen-Macaulay local ring admits only finitely many semidualizing modules up to isomorphism. We will describe the affirmative solution to this conjecture for any local ring (not necessarily Cohen-Macaulay). The proof uses a combination of techniques from commutative algebra, rational homotopy theory, and representation theory.

Original language | American English |
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State | Published - Mar 31 2012 |

Event | Spring Central Session Meeting of the American Mathematical Society, University of Kansas - Duration: Mar 31 2012 → … |

### Conference

Conference | Spring Central Session Meeting of the American Mathematical Society, University of Kansas |
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Period | 03/31/12 → … |

## Keywords

- Affirmative solution
- Cohen-Macaulay local ring
- Commutative algebra
- Finitely generated modules
- Isomorphism
- Local ring homomorphism
- Rational homotopy theory
- Representation theory
- Semidualizing modules

## DC Disciplines

- Mathematics