2006/01/10 by Klaus Hulek, Remke Kloosterman, Hulek, Klaus +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.math/0601207
Modified some proofs
openalex publication_date 2006/01/10 · arxiv created 2006/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the L-series of cubic fourfolds. Our main result is that, if X/C is a special cubic fourfold associated to some polarized K3 surface S, defined over a number field K such that S^[2](K) is not empty, then X has a model over K such that the L-series of the primitive cohomology of X/K can be expressed in the L-series of S/K. This allows us to compute the L-series for a discrete dense subset of cubic fourfolds in the moduli spaces of certain special cubic fourfolds. We also discuss a concrete example.