For strongly Z^2-graded rings, a chain complex is R_{(0,0)}-finitely dominated iff it is acyclic after base change to eight graded Novikov rings.
Finite domination and N ovikov homology over strongly Z -graded rings
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A modified fundamental theorem for algebraic K-theory is established for strongly Z-graded rings, with splittings via shift actions on modules and nil groups identified as reduced K-theory of homotopy nilpotent twisted endomorphisms, plus Mayer-Vietoris and localisation sequences.
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Finite domination and Novikov homology over strongly $\mathbb{Z}^2$-graded rings
For strongly Z^2-graded rings, a chain complex is R_{(0,0)}-finitely dominated iff it is acyclic after base change to eight graded Novikov rings.
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The "fundamental theorem" for the algebraic $K$-theory of strongly $\mathbb{Z}$-graded rings
A modified fundamental theorem for algebraic K-theory is established for strongly Z-graded rings, with splittings via shift actions on modules and nil groups identified as reduced K-theory of homotopy nilpotent twisted endomorphisms, plus Mayer-Vietoris and localisation sequences.