English

Arithmetic diagonal cycles on unitary Shimura varieties

Number Theory 2020-04-28 v6 Algebraic Geometry Representation Theory

Abstract

We define variants of PEL type of the Shimura varieties that appear in the context of the Arithmetic Gan-Gross-Prasad conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global and semi-global) integral models of these Shimura varieties and formulate for them conjectures on arithmetic intersection numbers. We prove some of these conjectures in low dimension.

Keywords

Cite

@article{arxiv.1710.06962,
  title  = {Arithmetic diagonal cycles on unitary Shimura varieties},
  author = {Michael Rapoport and Brian Smithling and Wei Zhang},
  journal= {arXiv preprint arXiv:1710.06962},
  year   = {2020}
}

Comments

We removed all mention of an 'exotic level structure". Final version. To appear in Compositio Mathematica

R2 v1 2026-06-22T22:18:49.289Z