Absolute Poincar\'e duality in \'etale cohomology

TL;DR

This paper extends Poincaré duality in étale cohomology from smooth to regular schemes using trace maps for local complete intersection morphisms.

Contribution

It introduces a formalism of trace maps that generalizes Poincaré duality to a broader class of schemes in étale cohomology.

Findings

Poincaré duality holds for regular schemes in étale cohomology.

Trace maps are formalized for local complete intersection morphisms.

The approach broadens the applicability of duality in algebraic geometry.

Abstract

We extend Poincar\'e duality in \'etale cohomology from smooth schemes to regular ones. This is achieved via a formalism of trace maps for local complete intersection morphisms.