Wintenberger, Jean-Pierre Une généralisation d’un théorème de Tate-Sen-Ax. (A generalisation of a theorem of Tate-Sen-Ax). (French) Zbl 0692.13018 C. R. Acad. Sci., Paris, Sér. I 307, No. 2, 63-65 (1988). Summary: Let R be a normal noetherian domain, with fraction field F of characteristic 0. Suppose that the scheme Spec(R) admits a desingularisation. Let \(\bar F\) be an algebraic closure of F and \(\bar R\) the integral closure of R in \(\bar F\); let x be an element of R. We prove that the subring of the x-adic completion of \(\bar R\), composed of the elements which are fixed by the Galois group \(Gal(\bar F/F)\), is the x- adic completion of R. Cited in 1 Document MSC: 13J10 Complete rings, completion 13B05 Galois theory and commutative ring extensions Keywords:integral closure; completion; Galois group PDFBibTeX XMLCite \textit{J.-P. Wintenberger}, C. R. Acad. Sci., Paris, Sér. I 307, No. 2, 63--65 (1988; Zbl 0692.13018)