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Geometric aspects of representation theory for DG algebras: answering a question of Vasconcelos
Author(s) -
Nasseh Saeed,
SatherWagstaff Keri Ann
Publication year - 2017
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12055
Subject(s) - isomorphism (crystallography) , mathematics , pure mathematics , representation theory , quotient , variety (cybernetics) , algebraic group , commutative property , algebra over a field , ring (chemistry) , commutative ring , group (periodic table) , algebraic structure , algebraic number , mathematical analysis , physics , chemistry , crystal structure , statistics , quantum mechanics , crystallography , organic chemistry
Abstract We apply geometric techniques from representation theory to the study of homologically finite differential graded (DG) modules M over a finite dimensional, positively graded, commutative DG algebra U . In particular, in this setting we prove a version of a theorem of Voigt by exhibiting an isomorphism between the Yoneda Ext groupYExt U 1 ( M , M )and a quotient of tangent spaces coming from an algebraic group action on an algebraic variety. As an application, we answer a question of Vasconcelos from 1974 by showing that a local ring has only finitely many semidualizing complexes up to shift‐isomorphism in the derived category D ( R ) .