# Poincaré duality and unimodularity

• ### Yuri G. Zarhin

Pennsylvania State University, University Park, USA

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## Abstract

It is well known that the cup-product pairing on the complementary integral cohomology groups (modulo torsion) of a compact oriented manifold is unimodular. We prove a similar result for the $\ell$-adic cohomology groups of smooth algebraic varieties.