Jan 10, 2015 · A branch of algebra, dealing mainly with the study of the so-called $K$-functors ($K_0, K_1$, etc., cf. $K$-functor); it is a part of general linear algebra. It deals with the …

In algebra, the fundamental theorem of algebraic K -theory describes the effects of changing the ring of K -groups from a ring R to or . The theorem was first proved by Hyman Bass for and …

Pages in category "Algebraic K-theory" The following 22 pages are in this category, out of 22 total. This list may not reflect recent changes.

The story starts within algebraic geometry, when in 1957 Grothendieck de-ned K0 of an algebraic variety (which we now call the Grothendieck group of a variety) in order to prove a …

Feb 26, 2022 · In a wide sense, the term "K-theory" is used to denote the branch of mathematics that includes algebraic $ K $-theory and topological $ K $-theory, and it is characterized by …

In short, algebraic K K -theory starts with the observation that the dimension of vector spaces over a field is a very useful thing! The start is the study of the K0 K 0 group of a ring, which is «the …

Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring R instead of a field. […] Algebraic K-theory plays an important part in many areas of mathematics, …

K-theory was developed by Atiyah and Hirzebruch in the 1960s based on work of Grothendieck in algebraic geometry. It was introduced as a tool in C *-algebra theory in the early 1970s …

In this paper we intend to given a basic overview of algebraic K-theory, with the goal of demonstrating the significance of the Steinberg symbol. In section 2, we introduce projective …

In mathematics, and especially differential and algebraic geometry, K-stability is an algebro-geometric stability condition, for complex manifolds and complex algebraic varieties.The notion …

ALGEBRAIC K-THEORY: DEFINITIONS & PROPERTIES (TALK NOTES) JUN HOU FUNG 1. Brief history of the lower K-groups Reference: Grayson, \Quillen’s Work in Algebraic K-Theory" …

SOME BASICS OF ALGEBRAIC K-THEORY AARON LANDESMAN 1. INTRODUCTION: ALGEBRAIC AND TOPOLOGICAL K THEORY In this paper, we explore the basics of …

Quillen was able to calculate the K-theory of nite elds with this de nition, and Borel calculated the ranks of the rational K-groups of the ring of integers in a number eld (= nite extension of Q).

In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζ K (s), is a generalization of the Riemann zeta function (which is obtained in the case where K is …

Jun 3, 2020 · Algebraic K-theory has seen a fruitful development during the last three years. Part of this recent progress was driven by the use of ∞-categories and related techniques originally …

The first branch of algebraic graph theory involves the study of graphs in connection with linear algebra.Especially, it studies the spectrum of the adjacency matrix, or the Laplacian matrix of a …

to homotopy, called brave new rings. Algebraic K-theory of brave new rings provides a very interesting link between alge. raic K-theory of rings and ge-ometry. This note is divided into …