Nonexistence of arithmetic fake compact hermitian symmetric spaces of types other than An

TL;DR

This paper proves that, except for type An, there are no arithmetic fake compact hermitian symmetric spaces of other types when n is greater than 4.

Contribution

It establishes a nonexistence result for certain symmetric spaces, extending the classification of fake compact hermitian symmetric spaces.

Findings

No arithmetic fake compact hermitian symmetric spaces of types other than An for n>4.

The result narrows the possible types of such spaces.

Provides a classification constraint for hermitian symmetric spaces.

Abstract

We show that there are no arithmetic fake compact hermitian symmetric spaces of type other than An for n>4.