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Quaternionic algebraic cycles and reality


Authors: Pedro F. dos Santos and Paulo Lima-Filho
Journal: Trans. Amer. Math. Soc. 356 (2004), 4701-4736
MSC (2000): Primary 55P91; Secondary 19L47, 14C25
DOI: https://doi.org/10.1090/S0002-9947-04-03663-3
Published electronically: June 22, 2004
MathSciNet review: 2084395
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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 $Gal({\mathbb C} / {\mathbb R})$. Appropriate stabilizations of these spaces yield two equivariant spectra. The first one classifies Dupont/Seymour's quaternionic $K$-theory, and the other one classifies an equivariant cohomology theory ${\mathfrak Z}^*(-)$ which is a natural recipient of characteristic classes $KH^*(X) \to {\mathfrak Z}^*(X)$ for quaternionic bundles over Real spaces $X$.


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Additional Information

Pedro F. dos Santos
Affiliation: Departamento de Matemática, Instituto Superior Técnico, Lisbon, Portugal
Email: pedfs@math.ist.utl.pt

Paulo Lima-Filho
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: plfilho@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03663-3
Received by editor(s): October 9, 2001
Published electronically: June 22, 2004
Additional Notes: The first author was supported in part by FCT (Portugal) through program POCTI and grant POCTI/1999/MAT/34015. The second author was partially supported by the NSF
Article copyright: © Copyright 2004 American Mathematical Society

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