Coefficient fields and scalar extension in positive characteristic

Details Coefficient fields and scalar extension in positive characteristic Coefficient fields and scalar extension in positive characteristic

2004-11-15

arxiv.org/abs/math/0411323v2

Journal of Algebra 285 (2005), 819-834

Mathematics

Commutative Algebra

Final version

Scientific paper

10.1016/j.jalgebra.2004.11.009

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}.

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