On Euler-Poincare characteristics

TL;DR

This paper extends Laumon's result on Euler characteristics from algebraic to topological settings, providing a broader understanding of cohomological invariants with potential applications.

Contribution

It generalizes Laumon's theorem from $\, ext{l}$-adic cohomology to topological cohomology, broadening the scope of Euler characteristic comparisons.

Findings

Established a topological analogue of Laumon's $\, ext{l}$-adic result.

Demonstrated applications in topological cohomology.

Clarified the relationship between different cohomological Euler characteristics.

Abstract

It is well known that the Euler characteristic of the cohomology of a complex algebraic variety coincides with the Euler characteristic of its cohomology with compact support. An old result of G. Laumon asserts that a relative version of this statement is true in $\ell$-adic cohomology. The purpose of this note is to extend Laumon's result to the topological setting. Some applications are also discussed.