Quillen’s work in algebraic K-theory
نویسندگان
چکیده
We survey the genesis and development of higher algebraic K-theory by Daniel Quillen.
منابع مشابه
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We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin’s theory and Quillen’s + construction are developed. In the special case of algebras associated with unit simplices one recovers the usual algebraic K-groups, while the general case of lattice polytopes reveals many new aspects, governed by...
متن کاملRegularity of Structured Ring Spectra and Localization in K-theory
We introduce a new notion of regularity for structured ring spectra, and we prove, in the presence of this condition, the existence of new Blumberg–Mandell-type localization sequences for algebraic K-theory. In particular, we confirm a conjecture of Ausoni–Rognes on the behavior of K(KO) as well as a natural generalization of this conjecture to K(Tmf). An early success of Quillen’s algebraic K-...
متن کاملBruns And
We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin’s theory and Quillen’s + construction are developed. In the special case of algebras associated with unit simplices one recovers the usual algebraic K-groups, while the general case of lattice polytopes reveals many new aspects, governed by...
متن کاملDerived Representation Theory and the Algebraic K-theory of Fields
Quillen’s higher algebraic K-theory for fields F has been the object of intense study since their introduction in 1972 [26]. The main direction of research has been the construction of “descent spectral sequences” whose E2-term involved the cohomology of the absolute Galois groupGF with coefficients in the algebraic K–theory of an algebraically closed. The form of such a spectral sequence was c...
متن کامل2 Winfried Bruns And
We overview results from our experiment of merging two seemingly unrelated disciplines – higher algebraic K-theory of rings and the theory of lattice polytopes. The usual K-theory is the “theory of a unit simplex”. The text is based on the works [BrG1, BrG5, BrG6]. Further related results are found in [BrG2, BrG3, BrG4]. At the end of the paper we propose a general conjecture on the structure o...
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تاریخ انتشار 2012