Tropicalizations of locally symmetric varieties

Abstract

This paper provides a rigorous study of tropicalizations of locally symmetric varieties. We give applications beyond tropical geometry, to the cohomology of moduli spaces as well as to the cohomology of arithmetic groups. We study two cases in detail: the special unitary case, and the case of level structures on the moduli space ${\mathcal{A}}_g$ of abelian varieties.

60 pages, 1 figure. Reorganized to improve clarity