Poincar\'e duality and unimodularity

TL;DR

This paper extends the classical Poincaré duality, showing that the cup-product pairing on the dic cohomology groups of smooth algebraic varieties is unimodular, analogous to the manifold case.

Contribution

It proves a Poincare9 duality type result for dic cohomology of smooth algebraic varieties, establishing unimodularity similar to the classical topological case.

Findings

Cup-product pairing on dic cohomology is unimodular

Analogous Poincare9 duality holds for algebraic varieties

Extends classical duality results to algebraic geometry context

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.