Algebraic and Real K-theory of Algebraic varieties
| dc.creator | Karoubi, Max | |
| dc.creator | Weibel, Charles | |
| dc.date | 2005-09-19 | |
| dc.date.accessioned | 2026-07-07T06:18:11Z | |
| dc.date.available | 2026-07-07T06:18:11Z | |
| dc.description | Let V be a smooth variety defined over the real numbers. Every algebraic vector bundle on V induces a complex vector bundle on the underlying topological space V(C), and the involution coming from complex conjugation makes it a Real vector bundle in the sense of Atiyah. This association leads to a natural map from the algebraic K-theory of V to Atiyah's ``Real K-theory'' of V(C). Passing to finite coefficients Z/m, we show that the maps from K_n(V ; Z/m) to KR ^{-n}(V(C);Z/m) are isomorphisms when n is at least the dimension of V, at least when m is a power of two. Our key descent result is a comparison of the K-theory space of V with the homotopy fixed points (for complex conjugation) of the K-theory space of the complex variety V(C). When V is the affine variety of the d-sphere S, it turns out that KR*(V(C))=KO*(S). In this case we show that for all nonnegative n we have K_n(V ; Z/m) = KO^{-n}(S ; Z/m). | |
| dc.description | 38 pages ; see also http://www.math.jussieu.fr/~karoubi/ and http://www.math.rutgers.edu/~weibel/ | |
| dc.identifier | https://arxiv.org/abs/math/0509412 | |
| dc.identifier | http://arxiv.org/abs/math/0509412 | |
| dc.identifier | Topology 42, (2003) 715-742 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94647 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Algebraic Geometry | |
| dc.title | Algebraic and Real K-theory of Algebraic varieties | |
| dc.type | text |