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

On Demazure and local Weyl modules for affine hyperalgebras