### Poincare Duality for Algebraic Varieties., by Ivan A. Panin and Serge A. Yagunov

Given an oriented theory on algebraic varieties we supply every smooth
projective algebraic variety X with a fundamental class [X]. It is proven
that the cap-product with the class [X] provides an isomorphism between the
cohomology and the homology of the variety X.

The result holds for (co-)homology theories represented by oriented
T-spectra. In particular, this class includes Motivic Cohomology represented
by the Eilenberg-Mac Lane T-spectrum H and the algebraic cobordism
represented by T-spectrum MGL.

In case the ground field is the complex numbers and the theory is singular
(co-)homology (or more generally any theory represented by an oriented
spectrum) the constructed isomorphism coincides with the classical Poincare
Duality.

Ivan A. Panin <panin@pdmi.ras.ru>

Serge A. Yagunov <yagunov@pdmi.ras.ru>