Density of crystalline points on unitary Shimura varieties

TL;DR

This paper proves that crystalline points are densely distributed in the spectrum of the completed Hecke algebra associated with unitary Shimura varieties, advancing understanding of their arithmetic structure.

Contribution

It establishes the density of crystalline points in the spectrum of the completed Hecke algebra on unitary Shimura varieties, a novel result in the field.

Findings

Crystalline points are dense in the spectrum of the completed Hecke algebra.

The result applies specifically to unitary Shimura varieties.

This advances the understanding of the arithmetic and geometric properties of Shimura varieties.

Abstract

We prove that crystalline points are dense in the spectrum of the completed Hecke algebra on unitary Shimura varieties.