La conjecture de Tate enti\`ere pour les cubiques de dimension quatre

TL;DR

This paper proves the Tate conjecture for integral degree 4 classes on smooth cubic fourfolds over algebraic closures of fields finitely generated over their prime subfield, advancing understanding in algebraic geometry.

Contribution

It establishes the Tate conjecture for a new class of algebraic varieties, specifically smooth cubic fourfolds, in a setting previously unresolved.

Findings

Proof of the Tate conjecture for degree 4 classes on cubic fourfolds

Advancement in understanding algebraic cycles on complex hypersurfaces

Extension of Tate conjecture validity to new geometric contexts

Abstract

We prove the Tate conjecture for integral degree 4 classes on a smooth cubic hypersurface X of dimension 4 over an algebraic closure of a field finitely generated over its prime subfield.