Coefficient fields and scalar extension in positive characteristic
arXiv:math/0411323 · doi:10.1016/j.jalgebra.2004.11.009
Abstract
Let k be a perfect field of positive characteristic, k(t)_{per} the perfect closure of k(t) and A=k[[X_1,...,X_n]]. We show that for any maximal ideal N of A'=k(t)_{per}\otimes_k A, the elements in \hat{A'_N} which are annihilated by the "Taylor" Hasse-Schmidt derivations with respect to the X_i form a coefficient field of \hat{A'_N}.
Final version