In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. [1] It determines the rank of the group of units in the ring O K of …

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 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 …

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 …

In mathematics, given a ring R, the K-theory spectrum of R is an Ω-spectrum whose nth term is given by, writing for the suspension of R, = () +, where "+" means the Quillen's + construction. [1]

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 …

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 …

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

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" …

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).

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 …

group is called virtually cyclic if it contains a (finite or infinite) cyclic subgroup of finite index. Let G be any discrete group, and let yc be the family of virtually cyclic subgroups of. aK : E yc+ ^OrG …

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 …