Coefficient fields and scalar extension in positive characteristic

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}.Comment: Final versio

On Hasse--Schmidt derivations: the action of substitution maps

“…In Section 6 we show how the action of substitution maps allows us to express any HS-derivation in terms of a fixed one under some natural hypotheses. This result generalizes Theorem 2.8 in [3] and provides a conceptual proof of it.…”

“…Properties (1) and ( 2) in Definition 5 are clear. Let us see property (3). For each t ∈ t let us write:…”

“…In this section we show how the action of substitution maps allows us to express any HS-derivation in terms of a fixed one under some natural hypotheses. We will be concerned with (s, t m (s))-variate HS-derivations, where t m (s) = {α ∈ N The following theorem generalizes Theorem 2.8 in [3] to the case where Der k (A) is not necessarily a finitely generated A-module. The use of substitution maps makes its proof more conceptual.…”