DG Homological Algebra and Solution to a Question of Vasconcelos

Saeed Nasseh; Sean Sather-Wagstaff

DG Homological Algebra and Solution to a Question of Vasconcelos

Saeed Nasseh, Sean Sather-Wagstaff

Mathematical Sciences

North Dakota State University

Research output: Contribution to conference › Presentation

Abstract

A homologically finite complex C over a commutative noetherian ring R is semidualizing if R Hom R ( C , C )&simeq; R in ' D ( R ). In this talk, we answer a question of Vasconcelos from 1974 by showing that a local ring has only finitely many shift-isomorphism classes of semidualizing complexes. Our proof relies on certain aspects of deformation theory for DG modules over a finite dimensional DG algebra.

Original language	American English
State	Published - Jan 10 2013
Event	AMS Special Session on Homotopy Theory and Commutative Algebra, Joint Mathematical Meetings - Duration: Jan 10 2013 → …

Conference

Conference	AMS Special Session on Homotopy Theory and Commutative Algebra, Joint Mathematical Meetings
Period	01/10/13 → …

Keywords

Commutative Noetherian ring
DG algebra
DG modules
Deformation theory
Homologically finite complex
Semidualizing
Semidualizing complexes
Shift-isomorphism classes

DC Disciplines

Mathematics

Cite this

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title = "DG Homological Algebra and Solution to a Question of Vasconcelos",

abstract = " A homologically finite complex C over a commutative noetherian ring R is semidualizing if R Hom R ( C , C )&simeq; R in ' D ( R ). In this talk, we answer a question of Vasconcelos from 1974 by showing that a local ring has only finitely many shift-isomorphism classes of semidualizing complexes. Our proof relies on certain aspects of deformation theory for DG modules over a finite dimensional DG algebra.",

keywords = "Commutative Noetherian ring, DG algebra, DG modules, Deformation theory, Homologically finite complex, Semidualizing, Semidualizing complexes, Shift-isomorphism classes",

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

note = "Saeed Nasseh and Sean Sather-Wagstaff. {"}DG Homological Algebra and Solution to a Question of Vasconcelos{"} AMS Special Session on Homotopy Theory and Commutative Algebra, Joint Mathematical Meetings. San Diego, CA. Jan. 2013. source:http://jointmathematicsmeetings.org/amsmtgs/2141_abstracts/1086-13-1077.pdf; AMS Special Session on Homotopy Theory and Commutative Algebra, Joint Mathematical Meetings ; Conference date: 10-01-2013",

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language = "American English",

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TY - CONF

T1 - DG Homological Algebra and Solution to a Question of Vasconcelos

AU - Nasseh, Saeed

AU - Sather-Wagstaff, Sean

N1 - Saeed Nasseh and Sean Sather-Wagstaff. "DG Homological Algebra and Solution to a Question of Vasconcelos" AMS Special Session on Homotopy Theory and Commutative Algebra, Joint Mathematical Meetings. San Diego, CA. Jan. 2013. source:http://jointmathematicsmeetings.org/amsmtgs/2141_abstracts/1086-13-1077.pdf

PY - 2013/1/10

Y1 - 2013/1/10

N2 - A homologically finite complex C over a commutative noetherian ring R is semidualizing if R Hom R ( C , C )&simeq; R in ' D ( R ). In this talk, we answer a question of Vasconcelos from 1974 by showing that a local ring has only finitely many shift-isomorphism classes of semidualizing complexes. Our proof relies on certain aspects of deformation theory for DG modules over a finite dimensional DG algebra.

AB - A homologically finite complex C over a commutative noetherian ring R is semidualizing if R Hom R ( C , C )&simeq; R in ' D ( R ). In this talk, we answer a question of Vasconcelos from 1974 by showing that a local ring has only finitely many shift-isomorphism classes of semidualizing complexes. Our proof relies on certain aspects of deformation theory for DG modules over a finite dimensional DG algebra.

KW - Commutative Noetherian ring

KW - DG algebra

KW - DG modules

KW - Deformation theory

KW - Homologically finite complex

KW - Semidualizing

KW - Semidualizing complexes

KW - Shift-isomorphism classes

M3 - Presentation

T2 - AMS Special Session on Homotopy Theory and Commutative Algebra, Joint Mathematical Meetings

Y2 - 10 January 2013

ER -

DG Homological Algebra and Solution to a Question of Vasconcelos

Abstract

Conference

Keywords

DC Disciplines

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