Geodesic
Non-commutative localisation and finite domination over strongly $\mathbb{Z}$-graded rings
Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 373-398.

Voir la notice de l'article provenant de la source International Press of Boston

Let $R = \bigoplus^{\infty}_{ k =-\infty} R_k$ be a strongly $\mathbb{Z}$-graded ring, and let $C^{+}$ be a chain complex of modules over the positive subring $P = \bigoplus^{\infty}_{k=0} R_k$. The complex $C^{+} \oplus_P R_0$ is contractible (resp., $C^{+}$ is $R_0$-finitely dominated) if and only if $C^{+} \oplus_P L$ is contractible, where $L$ is a suitable non-commutative localisation of $P$. We exhibit universal properties of these localisations, and show by example that an $R_0$-finitely dominated complex need not be $P$-homotopy finite.
DOI : 10.4310/HHA.2022.v24.n1.a18
Classification : 16E99, 16W50, 18G35, 55U15
Keywords: non-commutative localisation, finite domination, type FP, strongly graded ring, Novikov homology, algebraic mapping torus, Mather trick 
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     title = {Non-commutative localisation and finite domination over strongly $\mathbb{Z}$-graded rings},
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     pages = {373--398},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a18/}
}
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Thomas Hüttemann. Non-commutative localisation and finite domination over strongly $\mathbb{Z}$-graded rings. Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 373-398. doi : 10.4310/HHA.2022.v24.n1.a18. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a18/

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