English

Geometric and arithmetic theta correspondences

Number Theory 2025-03-11 v2 Algebraic Geometry Representation Theory

Abstract

Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. We give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also known as the Kudla program) and their applications. These are expanded lecture notes for the IHES 2022 Summer School on the Langlands Program.

Keywords

Cite

@article{arxiv.2402.12159,
  title  = {Geometric and arithmetic theta correspondences},
  author = {Chao Li},
  journal= {arXiv preprint arXiv:2402.12159},
  year   = {2025}
}

Comments

29 pages. final version. To appear in the proceedings of the IHES 2022 Summer School on the Langlands Program

R2 v1 2026-06-28T14:53:10.587Z