Article
Contracting Endomorphisms and Dualizing Complexes
Czechoslovak Mathematical Journal
Document Type
Article
Publication Date
9-1-2015
DOI
10.1007/s10587-015-0212-3
Disciplines
- Education and
- Mathematics
Abstract
We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring R. Our focus is on homological properties of contracting endomorphisms of R, e.g., the Frobenius endomorphism when R contains a field of positive characteristic. For instance, in this case, when R is F-finite and C is a semidualizing R-complex, we prove that the following conditions are equivalent: (i) C is a dualizing R-complex; (ii) C ∼RHomR(nR,C) for some n > 0; (iii) GC-dimnR < ∞ and C is derived RHomR(nR,C)-reflexive for some n > 0; and (iv) GC-dimnR < ∞ for infinitely many n > 0.
Citation Information
Saeed Nasseh and Sean Sather-Wagstaff. "Contracting Endomorphisms and Dualizing Complexes" Czechoslovak Mathematical Journal Vol. 65 Iss. 3 (2015) p. 837 - 865 Available at: http://works.bepress.com/saeed_nasseh/31/
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