Algebraic K-theory of rings from a topological viewpoint.

Título inglés Algebraic K-theory of rings from a topological viewpoint.
Título español K-teoría algebraica de los anillos desde un punto de vista topológico.
Autor/es Arlettaz, Dominique
Organización Inst. Math. Univ. Lausanne, Lausanne, Suiza
Revista 0214-1493
Publicación 2000, 44 (1): 3-84, 102 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Because of its strong interaction with almost every part of pure mathematics, algebraic K-theory has had a spectacular development since its origin in the late fifties. The objective of this paper is to provide the basic definitions of the algebraic K-theory of rings and an overview of the main classical theorems. Since the algebraic K-groups of a ring R are the homotopy groups of a topological space associated with the general linear group over R, it is obvious that many general results follow from arguments from homotopy theory. This paper is essentially devoted to some of them: it explains in particular how methods from stable homotopy theory, group cohomology and Postnikov theory can be used in algebraic K-theory.
Clasificación UNESCO 120101
Palabras clave español Espacio de Grothendieck ; Categoría de grupos ; Categoría algebraica ; Grupos de homología
Código MathReviews MR1775748
Código Z-Math Zbl 0956.19003
Icono pdf Acceso al artículo completo