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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Equivariant semi-topological invariants, Atiyah's $ KR$-theory, and real algebraic cycles


Authors: Jeremiah Heller and Mircea Voineagu
Journal: Trans. Amer. Math. Soc. 364 (2012), 6565-6603
MSC (2010): Primary 19E15, 19E20, 14F43
Published electronically: July 12, 2012
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Abstract: We establish an Atiyah-Hirzebruch type spectral sequence relating real morphic cohomology and real semi-topological $ K$-theory and prove it to be compatible with the Atiyah-Hirzebruch spectral sequence relating Bredon cohomology and Atiyah's $ KR$-theory constructed by Dugger. An equivariant and a real version of Suslin's conjecture on morphic cohomology are formulated, proved to come from the complex version of Suslin conjecture and verified for certain real varieties. In conjunction with the spectral sequences constructed here, this allows the computation of the real semi-topological $ K$-theory of some real varieties. As another application of this spectral sequence we give an alternate proof of the Lichtenbaum-Quillen conjecture over $ \mathbb{R}$, extending an earlier proof of Karoubi and Weibel.


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Additional Information

Jeremiah Heller
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730
Address at time of publication: Fachbereich C, Mathematik und Informatik, Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
Email: heller@math.northwestern.edu, heller@math.uni-wuppertal.de

Mircea Voineagu
Affiliation: Institute for Physics and Mathematics of the Universe, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan
Email: voineagu@usc.edu, mircea.voineagu@ipmu.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05603-0
PII: S 0002-9947(2012)05603-0
Received by editor(s): August 22, 2010
Received by editor(s) in revised form: April 3, 2011
Published electronically: July 12, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.