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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 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 R ^ that...

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