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