Displaying similar documents to “On the Jung method in positive characteristic”

Local monomialization of transcendental extensions

Steven Dale CUTKOSKY (2005)

Annales de l’institut Fourier

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Suppose that R ⊂ S are regular local rings which are essentially of finite type over a field k of characteristic zero. If V is a valuation ring of the quotient field K of S which dominates S , then we show that there are sequences of monoidal transforms (blow ups of regular primes) R → R 1 and S → S 1 along V such that R 1 → S 1 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. ...

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

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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...

Improvement of Grauert-Riemenschneider's theorem for a normal surface

Jean Giraud (1982)

Annales de l'institut Fourier

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Let X ˜ be a desingularization of a normal surface X . The group Pic ( X ˜ ) is provided with an order relation L ≫ _ 0 , defined by L . V ≤ 0 for any effective exceptional divisor V . Comparing to the usual order relation we define the ceiling of L which is an exceptional divisor. This notion allows us to improve the usual vanishing theorem and we deduce from it a numerical criterion for rationality and a genus formula for a curve on a normal surface; the difficulty lies in the case of a Weil divisor which...

Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains

Yong HU (2012)

Annales de l’institut Fourier

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Let R be a 2-dimensional normal excellent henselian local domain in which 2 is invertible and let L and k be its fraction field and residue field respectively. Let Ω R be the set of rank 1 discrete valuations of L corresponding to codimension 1 points of regular proper models of Spec R . We prove that a quadratic form q over L satisfies the local-global principle with respect to Ω R in the following two cases: (1) q has rank 3 or 4; (2) q has rank ≥ 5 and R = A [ [ y ] ] , where A is a complete discrete valuation...

When does the F -signature exist?

Ian M. Aberbach, Florian Enescu (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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We show that the F -signature of an F -finite local ring R of characteristic p > 0 exists when R is either the localization of an N -graded ring at its irrelevant ideal or Q -Gorenstein on its punctured spectrum. This extends results by Huneke, Leuschke, Yao and Singh and proves the existence of the F -signature in the cases where weak F -regularity is known to be equivalent to strong F -regularity.