Corpos de definição de grupos hiperbólicos complexos emdimensão 3

Abstract

Let (...) be a subgroup of (...). Let F be a subfield of C, the field of complex numbers. The field F is called a spliting field for (...) if (...) is conjugate in (...) to a subgroup in (...). The main result of this work is the following theorem. Theorem. Let (...) be a totally irreducible subgroup of (...). Then there exists a loxodromic element (...) with all its eigenvalues distinct such that (...) is conjugate in (...) to a subgroup of (...), where (...) is the field generated by the trace field (...) of (...) and the set of all eigenvalues of A. This theorem implies the following: Theorem. Let (...) be a totally irreducible subgroup of (...). Then the eigenvalue field (...) of (...), the field generated over Q by the eigenvalues of all the elements of (...),is a splitting field of (...). Theorem. Let (...) be a lattes in (...). Then (...) is a splitting field of (...).