Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories

被引：0

作者：

Eberhardt, Jens Niklas ^{[1
]}

Lorscheid, Oliver ^{[2
,3
]}

Young, Matthew B. ^{[4
]}

机构：

[1] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

[2] Univ Groningen, Groningen, Netherlands

[3] IMPA, Rio De Janeiro, Brazil

[4] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2022年 / 226卷 / 08期

关键词：

Algebraic K-theory; Grothendieck-Witt theory; Proto-exact categories;

D O I：

10.1016/j.jpaa.2022.107018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the algebraic K-theory and Grothendieck-Witt theory of proto-exact categories, with a particular focus on classes of examples of F-1-linear nature. Our main results are analogues of theorems of Quillen and Schlichting, relating the K- theory or Grothendieck-Witt theory spaces of proto-exact categories defined using the (hermitian) Q-construction and group completion. (c) 2022 The Author(s). Published by Elsevier B.V.& nbsp;

引用

页数：32

共 50 条

[41] Witt vectors and K-theory of automorphisms via noncommutative motives
Tabuada, Goncalo
MANUSCRIPTA MATHEMATICA, 2014, 143 (3-4) : 473 - 482
[42] A note on Milnor-Witt K-theory and a theorem of Suslin
Hutchinson, Kevin
Tao, Liqun
COMMUNICATIONS IN ALGEBRA, 2008, 36 (07) : 2710 - 2718
[43] A1-respresentability of hermitian K-theory and Witt groups
Hornbostel, J
TOPOLOGY, 2005, 44 (03) : 661 - 687
[44] Witt, GW, K-theory of quasi-projective schemes
Mandal, Satya
JOURNAL OF PURE AND APPLIED ALGEBRA, 2017, 221 (02) : 286 - 303
[45] THEORY OF G-CATEGORIES TOWARD EQUIVARIANT ALGEBRAIC K-THEORY
NIWA, M
JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1991, 31 (04): : 1023 - 1062
[46] EQUIVARIANT K-THEORY AND COMPLETION THEORY FOR CERTAIN CLASSIFYING-SPACES
AROUCHE, A
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1995, 320 (01): : 65 - 68
[47] HOMOTOPY EXACT SEQUENCE IN ALGEBRAIC K-THEORY
WEIBEL, CA
COMMUNICATIONS IN ALGEBRA, 1978, 6 (16) : 1635 - 1646
[48] ON THE K-THEORY AND HOMOTOPY THEORY OF THE KLEIN BOTTLE GROUP
Harlander, Jens
Misseldine, Andrew
HOMOLOGY HOMOTOPY AND APPLICATIONS, 2011, 13 (02) : 63 - 72
[49] K-THEORY FOR TWISTED GROUP RINGS
WILSON, SMJ
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1974, 29 (SEP) : 257 - 271
[50] The K-theory of Twisted Group Algebras
Echterhoff, Siegfried
C(ASTERISK)-ALGEBRAS AND ELLIPTIC THEORY II, 2008, : 67 - 86

← 1 2 3 4 5 →