Geodesic
Homology pro stability for Tor-unital pro rings
Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 343-374.

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

Let ${\lbrace A_m \rbrace}_m$ be a pro system of associative commutative, not necessarily unital, rings. Assume that the pro systems of Tor-groups ${\lbrace \operatorname{Tor}^{\mathbb{Z} \ltimes A_m}_{i} (\mathbb{Z}, \mathbb{Z}) \rbrace }_m$ vanish for all $i \gt 0$. Then we prove that the pro systems ${\lbrace H_l (\operatorname{GL}_n (A_m)) \rbrace }_m$ stabilize up to pro isomorphisms for $n$ large enough relative to $l$ and the stable range of $A_m$’s.
DOI : 10.4310/HHA.2020.v22.n1.a20
Classification : 13D15, 16E20, 19B14
Keywords: homology stability, $K$-theory excision, Tor-unitality 
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     author = {Ryomei Iwasa},
     title = {Homology pro stability for {Tor-unital} pro rings},
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     pages = {343--374},
     publisher = {mathdoc},
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     year = {2020},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n1.a20/}
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Ryomei Iwasa. Homology pro stability for Tor-unital pro rings. Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 343-374. doi : 10.4310/HHA.2020.v22.n1.a20. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n1.a20/

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