A Local Ring Has Only Finitely Many Semidualizing Complexes up to Isomorphism

Sean Sather-Wagstaff; Saeed Nasseh

A Local Ring Has Only Finitely Many Semidualizing Complexes up to Isomorphism

Sean Sather-Wagstaff, Saeed Nasseh

Mathematical Sciences

North Dakota State University

Research output: Contribution to conference › Presentation

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
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
Period	03/31/12 → …

Disciplines

Mathematics

Keywords

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

Cite this

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title = "A Local Ring Has Only Finitely Many Semidualizing Complexes up to Isomorphism",

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.",

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

author = "Sean Sather-Wagstaff and Saeed Nasseh",

note = "Sean Sather-Wagstaff and Saeed Nasseh. {"}A Local Ring Has Only Finitely Many Semidualizing Complexes up to Isomorphism{"} Spring Central Session Meeting of the American Mathematical Society, University of Kansas. Lawrence, KS. Mar. 2012. source:http://www.ams.org/amsmtgs/2187_abstracts/1081-13-221.pdf; Spring Central Session Meeting of the American Mathematical Society, University of Kansas ; Conference date: 31-03-2012",

year = "2012",

month = mar,

day = "31",

language = "American English",

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TY - CONF

T1 - A Local Ring Has Only Finitely Many Semidualizing Complexes up to Isomorphism

AU - Sather-Wagstaff, Sean

AU - Nasseh, Saeed

N1 - Sean Sather-Wagstaff and Saeed Nasseh. "A Local Ring Has Only Finitely Many Semidualizing Complexes up to Isomorphism" Spring Central Session Meeting of the American Mathematical Society, University of Kansas. Lawrence, KS. Mar. 2012. source:http://www.ams.org/amsmtgs/2187_abstracts/1081-13-221.pdf

PY - 2012/3/31

Y1 - 2012/3/31

N2 - 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.

AB - 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.

KW - Affirmative solution

KW - Cohen-Macaulay local ring

KW - Commutative algebra

KW - Finitely generated modules

KW - Isomorphism

KW - Local ring homomorphism

KW - Rational homotopy theory

KW - Representation theory

KW - Semidualizing modules

M3 - Presentation

T2 - Spring Central Session Meeting of the American Mathematical Society, University of Kansas

Y2 - 31 March 2012

ER -

A Local Ring Has Only Finitely Many Semidualizing Complexes up to Isomorphism

Abstract

Conference

Disciplines

Keywords

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