Geometric aspects of representation theory for DG algebras: answering\n a question of Vasconcelos

2011/12/29 by Saeed Nasseh, Nasseh, Saeed, Sean Sather-Wagstaff +1 · 1 citation
Mathematics · #13D02 #13D09 #13E10 #14L30 #16G30 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1201.0037

openalex publication_date 2011/12/29 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We apply geometric techniques from representation theory to the study of\nhomologically finite differential graded (DG) modules M over a finite\ndimensional, positively graded, commutative DG algebra U. In particular, in\nthis setting we prove a version of a theorem of Voigt by exhibiting an\nisomorphism between the Yoneda Ext group \YExt¹_U(M,M) and a\nquotient of tangent spaces coming from an algebraic group action on an\nalgebraic variety. As an application, we answer a question of Vasconcelos from\n1974 by showing that a local ring has only finitely many semidualizing\ncomplexes up to shift-isomorphism in the derived category \D(R).\n

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