A generalisation of the Abhyankar Jung theorem to associated graded rings of valuations

作者：Cutkosky Steven Dale^*

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2016, 160(2): 233-255.

DOI：10.1017/S0305004115000687

Suppose that R -> S is an extension of local domains and v* is a valuation dominating S. We consider the natural extension of associated graded rings along the valuation gr(v*) (R) -> gr(v*) (S). We give examples showing that in general, this extension does not share good properties of the extension R -> S, but after enough blow ups above the valuations, good properties of the extension R -> S are 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.

• 出版日期2016-3