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1University of Bielefeld, SFB-701, Postfach 100131, 33501 Bielefeld, Germany. e-mail: panin@math.uni-bielefeld.de
2Steklov Mathematical Institute (St. Petersburg), Fontanka 27, 191023 St. Petersburg, Russia. e-mail: panin@pdmi.ras.ru
1Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
2Steklov Mathematical Institute (St. Petersburg), Fontanka 27, 191023 St. Petersburg, Russia. e-mail: yagunov@gmail.com
Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2008, Issue 617, Pages 193–213, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2008.030, May 2008
Frank Adams introduced the notion of a complex oriented cohomology theory represented by a commutative ring spectrum and proved the Poincaré Duality Theorem for this general case. In the current paper we consider oriented cohomology theories on algebraic varieties represented by symmetric commutative ring T-spectra and prove the Duality Theorem, which mimics the result of Adams. This result is held, in particular, for Motivic Cohomology and Algebraic Cobordism of Voevodsky.
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