Article contents
A note on the Witt group and the KO-theory of complex Grassmannians
Published online by Cambridge University Press: 22 March 2011
Abstract
For a complex Grassmannian X, there is an isomorphism
between Balmer's Witt group and the quotient of topological K-theories.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © ISOPP 2011
References
At-Bo-Sh.Atiyah, M., Bott, R. and Shapiro, A.. Clifford modules. Topology 3 (1964) 3–38.CrossRefGoogle Scholar
Ba-Ca1.Balmer, P. and Calmès, B.Geometric description of the connecting homomorphism for Witt groups. Doc. Math. 14 (2009) 525–550.CrossRefGoogle Scholar
Ba-Ca2.Balmer, P. and Calmès, B.. Witt groups of Grassmann varieties. www.math.uiuc.edu/K-theory/903 (2008).Google Scholar
Ba-Wa.Balmer, P. and Walter, C.. A Gersten-Witt spectral sequence for regular schemes. Ann.Scient.Éc.Norm.Sup. 35 (2002) 127–152.CrossRefGoogle Scholar
Br.Brosnan, P.. Steenrod operations in Chow theory. Trans. of Amer. Math. Soc. 355 (2003) 1869–1903.CrossRefGoogle Scholar
Ca-Ho.Calmès, B. and Hornbostel, J.. Witt motives, transfers and devissage. preprint. (2006).Google Scholar
Fu.Fulton, W.. Intersection theory, second ed. Ergebnisse der Mathematic und ihrer Grenzgebiete. 3 Springer-Verlag, Berlin. (1998).Google Scholar
Gi.Gille, S.. A graded Gersten-Witt complex for schemes with a dualizing complex and the Chow group. J. Pure and Apllied Algebra 208 (2007) 391–419.CrossRefGoogle Scholar
Ha.Hara, S.. Note on KO-theory of BO(n) and BU(n). J. Math. Kyoto Univ. 31 (1991) 487–493.Google Scholar
Ho.Hornbostel, J..
-representability of hermitian K-theory and Witt group. Topology. 44 (2005) 661–687.CrossRefGoogle Scholar
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20151019112529662-0302:S1865243309999147_inline1.gif?pub-status=live)
Ko-Ha.Kono, A. and Hara, S.. KO-theory of complex Grassmannian. J. Math. Kyoto Univ. 31 (1991) 827–833.Google Scholar
La.Laksov, D.. Algebraic cycles on Grassmann varieties. Adv. in Math. 9 (1972) 267–295.CrossRefGoogle Scholar
Ne.Nenashev, A.. Gysin maps in Balmer-Witt theory. J. Pure and Appl. Algebra. 211 (2007) 203–221.Google Scholar
Or-Vi-Vo.Orlov, D., Vishik, A. and Voevodsky, V.. An exact sequence for Milnor's K-theory with applications to quadratic forms. Ann of Math. 165 (2007) 1–13.CrossRefGoogle Scholar
Pa.Pardon, W.. The filtered Gersten-Witt complex for regular schemes. www.math.uiuc.edu/K-theory/0419 (2000).Google Scholar
To.Totaro, B.. Non-injectivity of the map from the Witt group of a variety to the Witt group of its function field. J. Inst. Math. Jussieu 2 (2003) 483–493.CrossRefGoogle Scholar
Vo2.Voevodsky, V.. Motivic cohomology are isomorphic to higher Chow groups. www.math.uiuc.edu/K-theory/378 (1999).Google Scholar
Vo3.Voevodsky, V.. Reduced power operations in motivic cohomology. Publ.Math. IHES. 98 (2003) 1–54.Google Scholar
Ya.Yagita, N.. Motivic cohomology of quadrics and the coniveau spectral sequence. J. K-theory 6 (2010) 547–589.CrossRefGoogle Scholar
- 1
- Cited by