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Currently displaying 1 – 7 of 7

Order by Relevance | Title | Year of publication

Sur l'équation fonctionnelle de la fonction thêta de Riemann

Laurent Moret-Bailly — 1990

Compositio Mathematica

Variétés stablement rationnelles non rationnelles

Laurent Moret-Bailly

Séminaire Bourbaki

La formule de Noether pour les surfaces arithmétiques.

Laurent Moret-Bailly — 1989

Inventiones mathematicae

Un problème de descente

Laurent Moret-Bailly — 1996

Bulletin de la Société Mathématique de France

Groupes de Picard et problèmes de Skolem. I

Laurent Moret-Bailly — 1989

Annales scientifiques de l'École Normale Supérieure

Groupes de Picard et problèmes de Skolem. II

Laurent Moret-Bailly — 1989

Annales scientifiques de l'École Normale Supérieure

Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0

Laurent Moret-Bailly; Alexandra Shlapentokh — 2009

Annales de l’institut Fourier

Let $K$ be a one-variable function field over a field of constants of characteristic 0. Let $R$ be a holomorphy subring of $K$ , not equal to $K$ . We prove the following undecidability results for $R$ : if $K$ is recursive, then Hilbert’s Tenth Problem is undecidable in $R$ . In general, there exist $x_{1}, ..., x_{n} \in R$ such that there is no algorithm to tell whether a polynomial equation with coefficients in $ℚ (x_{1}, ..., x_{n})$ has solutions in $R$ .

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