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Currently displaying 1 – 3 of 3

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Frobenius pour les sommes de Selberg.

Olivier Piltant — 1995

Mathematische Annalen

On the Jung method in positive characteristic

Olivier Piltant — 2003

Annales de l’institut Fourier

Let $\bar{X}$ be a germ of normal surface with local ring $\bar{R}$ covering a germ of regular surface $X$ with local ring $R$ of characteristic $p > 0$ . Given an extension of valuation rings $W / V$ birationally dominating $\bar{R} / R$ , we study the existence of a new such pair of local rings ${\bar{R}}^{'} / R^{'}$ birationally dominating $\bar{R} / R$ , such that $R^{'}$ is regular and ${\bar{R}}^{'}$ has only toric singularities. This is achieved when $W / V$ is defectless or when $[W : V]$ is equal to $p$

Un exemple effectif de gradué non noethérien associé à une valuation divisorielle

Vincent Cossart; Carlos Galindo; Olivier Piltant — 2000

Annales de l'institut Fourier

Soit $R = k [x, y, z]_{(x, y, z)}$ le localisé de l’anneau des polynômes à trois variables sur le corps $k$ de . Nous construisons une valuation divisorielle $ν$ de $R$ , nous calculons un système minimal de générateurs de la $k$ -algèbre ${gr}_{ν} (R)$ associée à la filtration $ν$ -adique. Ce système est infini : ${gr}_{ν} (R)$ n’est pas noethérien.

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