Spitzweck, Markus and Ostvaer, Paul Arne (2012) Motivic twisted K-theory. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 12 (1). pp. 565-599. ISSN 1472-2739,
Full text not available from this repository. (Request a copy)Abstract
This paper sets out basic properties of motivic twisted K-theory with respect to degree three motivic cohomology classes of weight one. Motivic twisted K-theory is defined in terms of such motivic cohomology classes by taking pullbacks along the universal principal BG(m)-bundle for the classifying space of the multiplicative group scheme G(m). We show a Kunneth isomorphism for homological motivic twisted K-groups computing the latter as a tensor product of K-groups over the K-theory of BG(m). The proof employs an Adams Hopf algebroid and a trigraded Tor-spectral sequence for motivic twisted K-theory. By adapting the notion of an E-infinity-ring spectrum to the motivic homotopy theoretic setting, we construct spectral sequences relating motivic (co)homology groups to twisted K-groups. It generalizes various spectral sequences computing the algebraic K-groups of schemes over fields. Moreover, we construct a Chern character between motivic twisted K-theory and twisted periodized rational motivic cohomology, and show that it is a rational isomorphism. The paper includes a discussion of some open problems.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ALGEBRAIC COBORDISM; LANDWEBER EXACTNESS; CHERN CLASSES; COHOMOLOGY; MODULES; SPECTRUM; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 May 2020 06:20 |
| Last Modified: | 25 May 2020 06:20 |
| URI: | https://pred.uni-regensburg.de/id/eprint/19478 |
Actions (login required)
 |
View Item |
