A class number formula for Picard modular surfaces

Original · EN

We investigate arithmetic aspects of the middle degree cohomology of compactified Picard modular surfaces X attached to the unitary similitude group GU(2,1) for an imaginary quadratic extension E/Q. We construct new Beilinson--Flach classes on X and compute their Archimedean regulator. We obtain a special value formula involving a non-critical L-value of the degree six standard L-function, a Whittaker period, and the regulator. This provides evidence for Beilinson's conjecture in this setting.