English

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 LL-functions associated to cuspidal automorphic representations of GU(2,1)\mathrm{GU}(2,1), 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

R2 v1 2026-07-01T06:27:53.812Z