On the commensurability of hyperbolic Coxeter groups

Abstract: In this paper we study the commensurability of hyperbolic Coxeter groups of finite covolume, providing three necessary conditions for commensurability. Moreover we tackle different topics around the field of definition of a hyperbolic Coxeter group: which possible fields can arise, how this field determines a range of possible dihedral angles of a Coxeter polyhedron and we provide two new sets of generators for quasi-arithmetic groups. This work is a concise version of chapters 4 and 5 of the author's Ph.D. thesis.