  We show that much of local class theory can be deduced from the
Dieudonn\'e-Manin structure theory for $F$-isocrystals on an algebraically
closed field of characteristic $p>0$. As a consequence we get a new proof of a
formula of Dwork for the norm residue symbol, as well as a "constructive" proof
of the local Shafarevich-Weil theorem. This last answers a question of Morava.
