Symplectic and orthogonal <i>K</i>-groups of the integers

Schlichting, Marco

doi:10.1016/j.crma.2019.08.001

Topology

Symplectic and orthogonal K-groups of the integers

Presented by: Claire Voisin

Schlichting, Marco ¹

¹ Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK

Comptes Rendus. Mathématique, Volume 357 (2019) no. 8, pp. 686-690.

Abstract
Résumé

We explicitly compute the homotopy groups of the topological spaces $B Sp {(Z)}^{+}$ , $B O_{\infty, \infty} {(Z)}^{+}$ , and $B O_{\infty} {(Z)}^{+}$ .

Nous calculons explicitement les groupes d'homotopie des espaces topologiques $B Sp {(Z)}^{+}$ , $B O_{\infty, \infty} {(Z)}^{+}$ et $B O_{\infty} {(Z)}^{+}$ .

Received: 2019-06-08
Accepted: 2019-08-05
Published online: 2019-08-01

DOI: 10.1016/j.crma.2019.08.001

Author's affiliations:

Schlichting, Marco ¹

¹ Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK

@article{CRMATH_2019__357_8_686_0,
     author = {Schlichting, Marco},
     title = {Symplectic and orthogonal {\protect\emph{K}-groups} of the integers},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {686--690},
     publisher = {Elsevier},
     volume = {357},
     number = {8},
     year = {2019},
     doi = {10.1016/j.crma.2019.08.001},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2019.08.001/}
}

TY  - JOUR
AU  - Schlichting, Marco
TI  - Symplectic and orthogonal K-groups of the integers
JO  - Comptes Rendus. Mathématique
PY  - 2019
SP  - 686
EP  - 690
VL  - 357
IS  - 8
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.crma.2019.08.001/
DO  - 10.1016/j.crma.2019.08.001
LA  - en
ID  - CRMATH_2019__357_8_686_0
ER  -

%0 Journal Article
%A Schlichting, Marco
%T Symplectic and orthogonal K-groups of the integers
%J Comptes Rendus. Mathématique
%D 2019
%P 686-690
%V 357
%N 8
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2019.08.001/
%R 10.1016/j.crma.2019.08.001
%G en
%F CRMATH_2019__357_8_686_0

Schlichting, Marco. Symplectic and orthogonal K-groups of the integers. Comptes Rendus. Mathématique, Volume 357 (2019) no. 8, pp. 686-690. doi : 10.1016/j.crma.2019.08.001. https://www.numdam.org/articles/10.1016/j.crma.2019.08.001/

References
Cited by

[1] Balmer, P. Triangular Witt groups. II. From usual to derived, Math. Z., Volume 236 (2001) no. 2, pp. 351-382

[2] Friedlander, E.M. Computations of K-theories of finite fields, Topology, Volume 15 (1976) no. 1, pp. 87-109

[3] Karoubi, M. Bott periodicity in topological, algebraic and Hermitian K-theory, Handbook of K-Theory, Vol. 1, 2, Springer, Berlin, 2005, pp. 111-137

[4] Milnor, J.; Husemoller, D. Symmetric Bilinear Forms, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 73, Springer-Verlag, New York, Heidelberg, 1973

[5] Rognes, J. $K_{4} (Z)$ is the trivial group, Topology, Volume 39 (2000) no. 2, pp. 267-281

[6] Schlichting, M. The Mayer–Vietoris principle for Grothendieck–Witt groups of schemes, Invent. Math., Volume 179 (2010) no. 2, pp. 349-433

[7] Schlichting, M. Hermitian K-theory, derived equivalences and Karoubi's fundamental theorem, J. Pure Appl. Algebra, Volume 221 (2017) no. 7, pp. 1729-1844

[8] Schlichting, M. Higher K-theory of forms I. From rings to exact categories, J. Inst. Math. Jussieu (2019) (in prees) | DOI

[9] M. Schlichting, Higher K-theory of forms II. From exact categories to chain complexes, in preparation.

[10] M. Schlichting, Higher K-theory of forms III. From chain complexes to derived categories, in preparation.

[11] M. Schlichting, Higher K-theory of forms for Dedekind domains, in preparation.

[12] Weibel, C. Algebraic K-theory of rings of integers in local and global fields (Friedlander, E.M.; Grayson, D.R., eds.), Handbook of K-Theory, Vol. 1, Springer, Berlin, 2005, pp. 139-190

Cited by Sources:

^☆ This work was partially funded by the Leverhulme Trust.