Local Conjugacy of Irreducible Hyperbolic Toral Automorphisms
  This paper is dedicated to the conjugacy problem in $GL(n,\Z)$ and its connection with algebraic number theory. This connection may be summed up in the Latimer-MacDuffee-Taussky Theorem, which, in a very broad sense, identifies the conjugacy relation in $GL(n,\Z)$ with the relation of arithmetic equivalence between certain ideals of algebraic numbers. The main purpouse is to clarify the link between a weaker relation between ideals, weak equivalence, and local conjugacy in $GL(n,\Z)$, i.e., the conjugacy of $GL(n,\Z)$ matrices in the groups $GL(n,\Z_{p})$ of invertible matrices over the $p$-adic integers. 
Lennard F Bakker, Pedro Martins Rodrigues, Miguel M. R. Moreira
math.NT math.DS