Finite domination and Novikov homology over strongly Z-graded rings
Thomas Huettemann, Luke Steers
TL;DR
This paper characterizes when a bounded chain complex over a strongly Z-graded ring is homotopy equivalent to a finitely generated projective complex over the degree zero part, extending known results for Laurent polynomial rings.
Contribution
It provides a homological criterion for finite domination over strongly Z-graded rings, generalizing previous results for twisted Laurent polynomial rings.
Findings
Homological characterization of finite domination over strongly Z-graded rings
Extension of known results from Laurent polynomial rings to broader classes
Conditions for homotopy equivalence to finitely generated projective complexes
Abstract
Let L be a strongly Z-graded ring, and let C be a bounded chain complex of finitely generated L-modules. We give a homological characterisation of when C is homotopy equivalent, over L_0, to a bounded complex of finitely generated projective L_0-modules, generalising known results for twisted Laurent polynomial rings.
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