  We find new lower bounds on the torsion orders of very general Fano
hypersurfaces over (uncountable) fields of arbitrary characteristic. Our
results imply that unirational parametrizations of most Fano hypersurfaces need
to have enormously large degree. Our results also hold in characteristic two,
where they solve the rationality problem for hypersurfaces under a logarithmic
degree bound, thereby extending a previous result of the author from
characteristic different from two to arbitrary characteristic.
