Coefficient fields and scalar extension in positive characteristic

2004/11/30 by M. Fernandez-Lebron, L. Narvaez-Macarro
Mathematics · #math.AC #msc:13F25 #msc:13N15 #msc:13B35 #msc:13A35

paper · pdf · doi:10.1016/j.jalgebra.2004.11.009

published as Journal of Algebra 285 (2005), 819-834 · Final version

arxiv created 2005/05/19 · arxiv updated 2009/12/01

Abstract

Let k be a perfect field of positive characteristic, k(t)_per the perfect closure of k(t) and A=k[[X₁,...,X_n]]. We show that for any maximal ideal N of A'=k(t)_per⊗_k A, the elements in A'_N which are annihilated by the "Taylor" Hasse-Schmidt derivations with respect to the X_i form a coefficient field of A'_N.

Related

• Hasse-Schmidt Derivations and Coefficient Fields in Positive Characteristics
• Approximation and algebraicity in positive characteristic Hahn fields
• A generalization of the Hasse-Arf theorem
• Artin-Schreier-Witt extensions and ramification breaks
• Witt vectors and separably closed fields with higher derivations