2025/10/09 by Shi, Linli
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2510.08708
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 L-functions associated to cuspidal automorphic representations of GU(2,1), thus deducing non-triviality of the motivic classes and providing evidence for Beilinson's conjectures.