×
Schlichting, Marco

Hermitian \(K\)-theory of exact categories. (English) Zbl 1328.19009

J. \(K\)-Theory 5, No. 1, 105-165 (2010).
Summary: We study the theory of higher Grothendieck-Witt groups, alias algebraic hermitian \(K\)-theory, of symmetric bilinear forms in exact categories, and prove additivity, cofinality, dévissage and localization theorems - preparing the ground for the theory of higher Grothendieck-Witt groups of schemes as developed in the author’s papers [Invent. Math. 179, No. 2, 349–433 (2010; Zbl 1193.19005); “Hermitian \(K\)-theory, derived equivalences and Karoubi’s fundamental theorem”, preprint, http://www.math.lsu.edu/~mschlich/research/prelim.html]. No assumption on the characteristic is being made.

Cited in 36 Documents

MSC:

19G38 Hermitian \(K\)-theory, relations with \(K\)-theory of rings
19D06 \(Q\)- and plus-constructions
19G12 Witt groups of rings

Keywords:

hermitian \(K\)-theory; Quillen \(K\)-theory; Q-construction; exact categories with duality

Citations:

Zbl 1193.19005
PDF BibTeX XML Cite
\textit{M. Schlichting}, J. \(K\)-Theory 5, No. 1, 105--165 (2010; Zbl 1328.19009)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Ranicki, Lower K- and L-theory, London Mathematical Society Lecture Note Series 178 (1992)
[2] Knus, Quadratic and Hermitian forms over rings, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 294 (1991)
[3] Karoubi, Ann. Sci. École Norm. Sup. (4) 7 pp 359– (1975)
[4] Hornbostel, J. London Math. Soc. (2) 70 pp 77– (2004)
[5] Hornbostel, >Topology 44 pp 661– (2005)
[6] Hornbostel, K-Theory 26 pp 139– (2002)
[7] Grayson, >J. Algebra 61 pp 463– (1979)
[8] Goerss, Simplicial homotopy theory, Progress in Mathematics 174 (1999) · Zbl 0927.55022
[9] Cárdenas, K-Theory 12 pp 165– (1997)
[10] Charney, >Michigan Math. J. 33 pp 169– (1986)
[11] Balmer, >Math. Z. 236 pp 351– (2001)
[12] Waldhausen, Algebraic and geometric topology (New Brunswick, N.J., 1983), Lecture Notes in Math. pp 318– (1126)
[13] Wagoner, Topology 11 pp 349– (1972)
[14] Scharlau, Quadratic and Hermitian forms, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 270 (1985)
[15] Quillen, Topology 10 pp 67– (1971)
[16] Quebbemann, J. Algebra 59 pp 264– (1979)
[17] Pedersen, Algebraic topology (Arcata, CA, 1986), Lecture Notes in Math. 1370 pp 346– (1989)
[18] Popescu, Abelian categories with applications to rings and modules 3 (1973) · Zbl 0271.18006
[19] Knebusch, Conference on Quadratic Forms–1976 (Proc. Conf., Queen’s Univ., Kingston, Ont. 46 pp 103– (1976)
[20] Keller, Handbook of algebra 1 pp 671– (1996)
[21] Keller, >Manuscripta Math. 67 pp 379– (1990)
[22] Karoubi, Ann. of Math. (2) 112 pp 207– (1980)
[23] Karoubi, Ann. of Math. (2) 112 pp 259– (1980)
[24] Uridia, K-theory and homological algebra (Tbilisi, 1987–88), Lecture Notes in Math. 1437 pp 303– (1990)
[25] Thomason, The Grothendieck Festschrift, Vol. III, Progr. Math. 88 pp 247– (1990)
[26] Schlichting, >Math. Z. 253 pp 97– (2006)
[27] Schlichting, K-Theory 32 pp 253– (2004)
[28] Schlichting, >Topology 43 pp 1089– (2004)
[29] Quillen, Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash. 341 pp 85– (1972) · Zbl 0292.18004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.