# Meeting Details

Title: Poincaré duality and unimodularity Algebra and Number Theory Seminar Yuri Zarhin, Penn State University 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 over an algebraically closed field, whose characteristic is different from $\ell$.