Abstract
AbstractSuppose thatR→Sis an extension of local domains andν* is a valuation dominatingS. We consider the natural extension of associated graded rings along the valuation grν*(R) → grν*(S). We give examples showing that in general, this extension does not share good properties of the extensionR→S, but after enough blow ups above the valuations, good properties of the extensionR→Sare reflected in the extension of associated graded rings. Stable properties of this extension (after blowing up) are much better in characteristic zero than in positive characteristic. Our main result is a generalisation of the Abhyankar–Jung theorem which holds for extensions of associated graded rings along the valuation, after enough blowing up.
Publisher
Cambridge University Press (CUP)
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