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Fibrations with few rational points

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If you have a question about this talk, please contact G. Rosso.

please note this seminar wil take place in MR12

We study the problem of counting the number of varieties in families which have a rational point. We give geometric conditions on the singular fibres that force very few of the varieties in the family to have a rational point, in a precise quantitative sense. This builds on ideas and techniques developed by Serre, and generalises and unifies existing results in the literature by Serre, Browning-Dietmann, Bright-Browning-Loughran, Graber-Harris-Mazur-Starr, … This is joint work with Daniel Loughran (Hannover).

This talk is part of the Number Theory Seminar series.

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