  We prove the Zorich-Kontsevich conjecture that the non-trivial Lyapunov
exponents of the Teichm\"uller flow on (any connected component of a stratum
of) the moduli space of Abelian differentials on compact Riemann surfaces are
all distinct. By previous work of Zorich and Kontsevich, this implies the
existence of the complete asymptotic Lagrangian flag describing the behavior in
homology of the vertical foliation in a typical translation surface.
