Linli Shi | Papers

Papers

Papers and preprints

My research focuses on the connections between automorphic forms, motivic cohomology, and special values of L-functions.

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, their relation to interior motives, and non-critical values of motivic L-functions associated with cuspidal automorphic representations of GU(2,1).

Picard modular surfaces Motivic cohomology Higher regulators Beilinson’s conjectures

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.

In preparation

Adelic Borcherds lifts and Borcherds products

Joint with Wenxuan Qi, Liang Xiao, and Yichao Zhang.
Theta lifts in higher Chow groups

Joint with Wenxuan Qi, Liang Xiao, and Yichao Zhang.
On higher regulators of orthogonal Shimura varieties

Joint with Wenxuan Qi, Liang Xiao, and Yichao Zhang.
On regularized linear periods

Joint with Pierre-Henri Chaudouard.
Higher Hida and Coleman theory on GU(2,1)

Joint with Zhengfu Chen.