Reflexivity and rigidity for complexes, I: Commutative rings

By L. Avramov, S. Iyengar, J. Lipman. 2009

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A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main results characterizes C-rigid complexes. Specialized to the case when C is the relative dualizing complex of a homomorphism of rings of finite Gorenstein dimension, it leads to broad generalizations of theorems of Yekutieli and Zhang concerning rigid dualizing complexes, in the sense of Van den Bergh. Along the way, new results about derived reflexivity with respect to C are established. Noteworthy is the statement that derived C-reflexivity is a local property; it implies that a finite R-module M has finite G-dimension over R if Mm has finite G-dimension over Rm for each maximal ideal m of R.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/870b8325a47e6adab794451998157e9019988b76

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In Algebra and Number Theory

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Citations in the corpus

Beyond totally reflexive modules and back (2008, background): “Generalized notions of G-dimension—based on reflexivity with respect to semidualizing modules and complexes—are studied by Avramov, Iyengar, and Lipman [ 18 ], Christensen [29], Frankild and Sather-Wagstaff [60], Gerko [61], Golod [62], Holm and Jorgensen [70], by Salarian, Sather-Wagstaff, and Yass”