Abstract
Let $S$ be an arithmetic quotient of a Hermitian symmetric domain and $X/S$ be a family of varieties over $S$. One interesting problem is to find the Hodge classes of $X$, and if possible, to prove the Hodge conjecture for $X$. Using techniques from automorphic forms, we studied the Hodge conjecture for certain families of varieties over arithmetic quotients of balls and the Siegel domain of degree two. As a byproduct, we derived formulas for Hodge numbers in terms of automorphic forms.
Committee Chair
Matt Kerr
Degree
Doctor of Philosophy (PhD)
Author's Department
Mathematics
Document Type
Dissertation
Date of Award
5-8-2024
Language
English (en)
DOI
https://doi.org/10.7936/ad78-xg54
Author's ORCID
0009-0000-6442-5153
Recommended Citation
Cheng, Xiaojiang, "Hodge Classes in the Cohomology of Local Systems" (2024). Arts & Sciences Theses and Dissertations. 3011.
The definitive version is available at https://doi.org/10.7936/ad78-xg54