On higher regulators of Picard modular surfaces
Number Theory
2025-10-13 v1 Algebraic Geometry
K-Theory and Homology
Representation Theory
Abstract
We prove the motivic classes in the motivic cohomology groups of Picard modular surfaces with non-trivial coefficients constructed in a paper of Loeffler\textendash Skinner\textendash Zerbes are in the motivic cohomology groups of the interior motives. Then we establish a relation between the motivic classes and non-critical values of the motivic -functions associated to cuspidal automorphic representations of , thus deducing non-triviality of the motivic classes and providing evidence for Beilinson's conjectures.
Keywords
Cite
@article{arxiv.2510.08708,
title = {On higher regulators of Picard modular surfaces},
author = {Linli Shi},
journal= {arXiv preprint arXiv:2510.08708},
year = {2025}
}
Comments
Based on the author's Ph.D. thesis at the University of Connecticut (2025); 100 pages. Comments welcome