A problem on coefficient fields and equations over local rings
M. Van der Put (1975)
Compositio Mathematica
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M. Van der Put (1975)
Compositio Mathematica
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Takako Kuzumaki (1991)
Compositio Mathematica
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Paolo Valabrega (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Steven Dale CUTKOSKY (2005)
Annales de l’institut Fourier
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Suppose that are regular local rings which are essentially of finite type over a field of characteristic zero. If is a valuation ring of the quotient field of which dominates , then we show that there are sequences of monoidal transforms (blow ups of regular primes) and along such that is a monomial mapping. It follows that a morphism of nonsingular varieties can be made to be a monomial mapping along a valuation, after blow ups of nonsingular subvarieties. ...
Steven Dale Cutkosky (1995)
Compositio Mathematica
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Steven Dale Cutkosky, Samar ElHitti (2010)
Annales de la faculté des sciences de Toulouse Mathématiques
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Suppose that is a local domain essentially of finite type over a field of characteristic , and a valuation of the quotient field of which dominates . The rank of such a valuation often increases upon extending the valuation to a valuation dominating , the completion of . When the rank of is , 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 , there is no natural ideal...