Hodge Classes in the Cohomology of Local Systems

2023/11/01 by Cheng, Xiaojiang
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.00243

Abstract

We study the Hodge conjecture for certain families of varieties over arithmetic quotients of balls and Siegel domain of degree two. As a byproduct, we derive formulas for Hodge numbers in terms of automorphic forms.

Related

• Non vanishing loci of Hodge numbers of local systems
• Mixed Hodge complexes and L²-cohomology for local systems on ball quotients
• Hodge numbers for the cohomology of Calabi-Yau type local systems
• The Hodge conjecture and arithmetic quotients of complex balls
• Hodge theory for local systems and cohomological support loci