2003/02/10 by Spencer Bloch, Bloch, Spencer, Hélène Esnault +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0302109
16 pages
arxiv created 2003/02/10 · openalex publication_date 2003/02/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X⊂ ¶n be a possibly singular hypersurface of degree d≤ n, defined over a finite field k. We show that the diagonal, suitably interpreted, is decomposable. This gives a proof that the eigenvalues of the Frobenius action on its ℓ-adic cohomology Hi(X, \Q_ℓ), for ℓ ≠ \rm char(k), are divisible by q, without using the result on the existence of rational points by Ax and Katz.