HIGHER K-THEORY OF FORMS I. FROM RINGS TO EXACT CATEGORIES

被引：10

作者：

Schlichting, Marco ^{[1
]}

机构：

[1] Univ Warwick, Math Inst, Marco Schlichting, Zeeman Bldg, Coventry CV4 7AL, W Midlands, England

来源：

JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU | 2021年 / 20卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

higher K-theory of forms; group completion; HOMOLOGY;

D O I：

10.1017/S1474748019000410

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the analog for the K-theory of forms of the Q = + theorem in algebraic K-theory. That is, we show that the K-theory of forms defined in terms of an S-center dot-construction is a group completion of the category of quadratic spaces for form categories in which all admissible exact sequences split. This applies for instance to quadratic and hermitian forms defined with respect to a form parameter.

引用

页码：1205 / 1273

页数：69

共 31 条

[1]

[Anonymous], 1973, ERGEBNISSE MATH IHRE

[2]

BAK A, 1981, ANN MATH STUDIES, V98

[3]

BASS H, 1968, ALGEBRAIC K THEORY

[4] QUADRATIC FUNCTORS AND METASTABLE HOMOTOPY [J].

BAUES, HJ .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1994, 91 (1-3) :49-107

[5]

Bouc S., 1997, LECT NOTES MATH, V1671

[6]

Bourbaki N., 2007, Elements de mathematique

[7]

BOUSFIELD AK, 1978, LECT NOTES MATH, V658, P80

[8]

CHARNEY R, 1986, MICH MATH J, V33, P169

[9]

Dotto E., IN PRESS

[10] Rings, modules, and algebras in infinite loop space theory [J].

Elmendorf, A. D. ;

Mandell, M. A. .

ADVANCES IN MATHEMATICS, 2006, 205 (01) :163-228

← 1 2 3 4 →