General Horizontal Norm Compatible Systems on unitary Shimura varieties

TL;DR

This paper aims to construct a new family of norm-compatible cycles related to Gross--Gan--Prasad cycles on unitary Shimura varieties, extending the understanding of special cycles in automorphic forms.

Contribution

It introduces a novel construction of norm-compatible families of cycles on unitary Shimura varieties for arbitrary dimensions, advancing the theory of special cycles and their arithmetic properties.

Findings

Construction of a new norm-compatible family of cycles.

Extension of Gross--Gan--Prasad cycles to higher dimensions.

Potential applications to automorphic forms and number theory.

Abstract

The ultimate goal of the paper is to construct a novel norm-compatible family of cycles appearing in the context of Gross--Gan--Prasad cycles arising from Shimura varieties attached to $U(n-1,1)\hookrightarrow U(n,1) \times U(n-1,1)$ for arbitrary $n$.