# Geometry and Arithmetic

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#### DOI: 10.4171/119-1/21

Poincaré duality and unimodularity

Yuri G. Zarhin[1]

(1) Pennsylvania State University, University Park, USA

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.

Keywords: Étale cohomology, Poincaré duality, perfect pairing