Linli Shi 师林立

Postdoctoral Researcher
Department of Mathematics, ETH Zürich
ETH Zürich and UniDistance Suisse
linli.shi@math.ethz.ch
linli-shi.github.io
Zürich, Switzerland

Papers

Research papers and preprints

My research interests include number theory, automorphic forms and arithmetic geometry. This page lists papers and preprints; for a broader overview, see my research profile.

Preprints

On higher regulators of Picard modular surfaces

arXiv:2510.08708. Submitted.

This paper studies motivic classes on Picard modular surfaces with non-trivial coefficients. It proves that the classes constructed by Loeffler--Skinner--Zerbes lie in the motivic cohomology of interior motives, and establishes a relation with non-critical values of motivic L-functions associated to cuspidal automorphic representations of GU(2,1).

Picard modular surfaces Motivic cohomology Interior motives Higher regulators Beilinson's conjectures Automorphic L-functions
Abstract

We prove that the motivic classes in the motivic cohomology groups of Picard modular surfaces with non-trivial coefficients constructed in work of Loeffler--Skinner--Zerbes lie in the motivic cohomology groups of the interior motives. We then establish a relation between these classes and non-critical values of motivic L-functions associated to cuspidal automorphic representations of GU(2,1), deducing non-triviality of the classes and providing evidence for Beilinson's conjectures.

Related reference: Loeffler--Skinner--Zerbes, An Euler system for GU(2,1).