Global smooth rigidity for toral automorphisms

We study regularity of a conjugacy between a hyperbolic or partially hyperbolic toral automorphism L and a C∞ diffeomorphism f of the torus. For a very weakly irreducible hyperbolic automorphism L we show that any C1 conjugacy is C∞. For a very weakly irreducible ergodic partially hyperbolic automorphism L we show that any C1+Hölder conjugacy is C∞. As a corollary, we improve regularity of the conjugacy to C∞ in prior local and global rigidity results.