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Une généralisation d’un théorème de Tate-Sen-Ax. (A generalisation of a theorem of Tate-Sen-Ax). (French) Zbl 0692.13018

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.

MSC:

13J10 Complete rings, completion
13B05 Galois theory and commutative ring extensions
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