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The probability that a complete intersection is smooth

Alina Bucur, Kiran S. Kedlaya (2012)

Journal de Théorie des Nombres de Bordeaux

Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension. This generalizes the case of a single hypersurface, due to Poonen. We use this result to give a probabilistic model for the number of rational points of such a complete intersection. A somewhat surprising corollary is that the number of rational points on a random smooth intersection...

Transversal crystals of finite level

Bernard Le Stum, Adolfo Quirós (1997)

Annales de l'institut Fourier

We extend Ogus’notion of T -crystal and F -span to the context of Berthelot’s crystals of level m and we study the generalization of Ogus’theorem on the equivalence between T -crystals and F -spans of width less than p .

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