Title: Quaternionic algebraic cycles and reality


Authors:

 
Pedro F. dos Santos (pedfs@math.ist.utl.pt)
Instituto Superior Técnico
Lisboa, Portugal

and

Paulo Lima-Filho (plfilho@math.tamu.edu)
Texas A&M university
College Station, Texas
USA

AMS classification: 55P91; Secondary 14C05, 19L47, 55N91

Abstract

In this paper we compute the equivariant homotopy type of spaces of 
algebraic cycles on real Brauer-Severi varieties, under the action 
of the Galois group  Gal(C/R). Appropriate stabilizations of these
spaces yield two equivariant spectra. The first one classifies Dupont/Seymour's
quaternionic K-theory, and the other one classifies and equivariant
cohomology theory Z^*(-) which is a natural recipient of
characteristic classes KH^*(X) --> Z^*(X) for quaternionic 
bundles over Real spaces X.