  We establish the existence of Demazure flags for graded local Weyl modules
for hyper current algebras in positive characteristic. If the underlying simple
Lie algebra is simply laced, the flag has length one, i.e., the graded local
Weyl modules are isomorphic to Demazure modules. This extends to the positive
characteristic setting results of Fourier-Littelmann and Naoi for current
algebras in characteristic zero. Using this result, we prove that the character
of local Weyl modules for hyper loop algebras depend only on the highest
weight, but not on the (algebraically closed) ground field, and deduce a tensor
product factorization for them.
