I will try to explain how a few of the arguments from Tao´s paper can be simplified and generalized, so that they work in all characteristics (over arbitrary fields). My arguments are quite straightforward and require only some knowledge of commutative algebra. Reference: Tao´s paper "Expanding polynomials over finite fields of large characteristic, and a regularity lemma for definable sets" (http://arxiv.org/abs/1211.2894).