Homotopy theory of rings and algebraic $K$-theory
نویسندگان
چکیده
منابع مشابه
Algebraic Homotopy Theory, Groups, and K-Theory
A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in The Faculty of Graduate Studies Department of Mathematics. LetMk be the category of algebras over a unique factorization domain k, and let ind−Affk denote the category of pro-representable functions from Mk to the category E of sets. It is shown that ind−Affk is a closed model category in such...
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We decompose the K-theory space of a Waldhausen category in terms of its Dwyer-Kan simplicial localization. This leads to a criterion for functors to induce equivalences of K-theory spectra that generalizes and explains many of the criteria appearing in the literature. We show that under mild hypotheses, a weakly exact functor that induces an equivalence of homotopy categories induces an equiva...
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Are all finitely generated projective k[t1, . . . , td]-modules free for an arbitrary field k and arbitrary d ∈ N? This question, set in Serre’s famous paper FAC in 1955, inspired an enormous activity of algebraists worldwide. The activity culminated in two independent confirmations of the question in 1976 by Quillen and Suslin. In the meanwhile the algebraic K-theory was created, in which one ...
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The main purpose of the present article is to establish the real case of “Karoubi’s Conjecture” [20] in algebraic K-theory. The complex case was proved in 1990-91 (cf. [32] for the C∗-algebraic form of the conjecture, and [38] for both the Banach and C∗-algebraic forms). Compared to the case of complex algebras, the real case poses additional difficulties. This is due to the fact that topologic...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1971
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1971-12626-5