Algebraic description of complex conjugation on cohomology of a smooth projective hypersurface

2024/02/22 by Jeehoon Park, Park, Jeehoon, Junyeong Park +3
Mathematics · #14C30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2402.14546

openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe complex conjugation on the primitive middle-dimensional algebraic de Rham cohomology of a smooth projective hypersurface defined over a number field that admits a real embedding. We use Griffiths' description of the cohomology in terms of a Jacobian ring. The resulting description is algebraic up to transcendental factors explicitly given by certain periods.

Related

• Complex conjugation and simplicial algebraic hypersurfaces
• Conjugate varieties with distinct real cohomology algebras
• From Sheaf Cohomology to the Algebraic de Rham Theorem
• Mixed Hodge Structures
• Motives and algebraic de rham cohomology