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Formal prime ideals of infinite value and their algebraic resolution

Steven Dale Cutkosky; Samar ElHitti — 2010

Annales de la faculté des sciences de Toulouse Mathématiques

Suppose that $R$ is a local domain essentially of finite type over a field of characteristic $0$ , and $ν$ a valuation of the quotient field of $R$ which dominates $R$ . The rank of such a valuation often increases upon extending the valuation to a valuation dominating $\hat{R}$ , the completion of $R$ . When the rank of $ν$ is $1$ , Cutkosky and Ghezzi handle this phenomenon by resolving the prime ideal of infinite value, but give an example showing that when the rank is greater than $1$ , there is no natural ideal in $\hat{R}$ that...

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