On the Tate conjecture for the Fano surfaces of cubic threefolds

2012/03/13 by Xavier Roulleau, Roulleau, Xavier
Mathematics · #14C25 #14F20 #14J29 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14C25 #msc:14F20 #msc:14J29

paper · pdf · doi:10.48550/arxiv.1203.2913

4 pages ; the first version of this paper has been split into two parts

openalex publication_date 2012/03/13 · arxiv created 2013/04/15 · arxiv updated 2013/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Fano surface of a smooth cubic threefold X in P⁴ parametrizes the lines on X. In this note, we prove that a Fano surface satisfies the Tate conjecture over a field of finite type over the prime field and characteristic not 2.

Related

• Lines on cubic threefolds and fourfolds containing a plane
• The zeta functions of the Fano surfaces of cubic threefolds
• Quotients of Fano Surfaces
• The motive of the Fano surface of lines
• The Tate Conjecture for Motivic Endomorphisms of K3 Surfaces over Finite Fields