Surjectivity of cycle maps for singular varieties

TL;DR

This paper extends Jannsen's theorem, originally for smooth projective varieties, to include singular quasi-projective varieties, showing conditions under which cycle class maps are surjective.

Contribution

It provides a new version of Jannsen's theorem applicable to singular quasi-projective varieties, broadening the scope of cycle map surjectivity results.

Findings

Surjectivity of cycle maps for singular quasi-projective varieties established

Extension of Jannsen's theorem to a broader class of varieties

Conditions under which cycle class maps are surjective identified

Abstract

A theorem of Jannsen asserts that if a smooth projective variety has injective cycle class maps, it has surjective cycle class maps. The object of this note is to present a version of Jannsen's theorem for singular quasi--projective varieties.