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Kasprowski, Daniel; Winges, Christoph

Shortening binary complexes and commutativity of \(K\)-theory with infinite products. (English) Zbl 07183274

Trans. Am. Math. Soc., Ser. B 7, 1-23 (2020).
Summary: We show that in Grayson’s model of higher algebraic \(K\)-theory using binary acyclic complexes, the complexes of length two suffice to generate the whole group. Moreover, we prove that the comparison map from Nenashev’s model for \(K_1\) to Grayson’s model for \(K_1\) is an isomorphism. It follows that algebraic \(K\)-theory of exact categories commutes with infinite products.

Cited in 1 Review
Cited in 2 Documents

MSC:

19D06 \(Q\)- and plus-constructions
18E10 Abelian categories, Grothendieck categories

Keywords:

shortening; binary acyclic complexes; algebraic \(K\)-theory of infinite products
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\textit{D. Kasprowski} and \textit{C. Winges}, Trans. Am. Math. Soc., Ser. B 7, 1--23 (2020; Zbl 07183274)
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References:

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