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+H\"older conjugacy is C^∞. As a corollary, we improve regularity of the conjugacy to C^∞ in prior local and global rigidity results.