2003/10/11 by Dinakar Ramakrishnan, Ramakrishnan, Dinakar · 1 citation
Mathematics · #11F41 #11G35 #14C25 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11F41 #msc:11G35 #msc:14C25 #msc:14G35
paper · pdf · doi:10.48550/arxiv.math/0310162
arxiv created 2003/10/11 · openalex publication_date 2003/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give some evidence for the Tate (and Hodge) conjecture(s) for a class of Hilbert modular fourfolds X, whose connected components arise as arithmetic quotients of the fourfold product of the upper half plane by congruence subgroups Γof SL(2, OK), where OK denotes the ring of integers of a quartic, Galois, totally real number field K. The expected relationship to the orders of poles of the associated L-functions is verified for abelian extensions of \Q. Also shown is the existence of homologically non-trivial cycles of codimension two which are not intersections of divisors.