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p-adic integrals and rational points on families of curves

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KA2W02 - Arithmetic geometry, cycles, Hodge theory, regulators, periods and heights

Caporaso, Harris and Mazur showed that Lang’s conjecture on rational points on varieties of general type implies a certain ‘arithmetic correlation’ between rational points on hyperbolic curves in families. More precisely, it implies that the rational points on a suitably large fibre power of the family are not Zariski dense. In this talk, we explain some arithmetic correlation results which can be proved for ‘low rank’ points, using a suitable notion of p-adic integration or p-adic period maps.

This talk is part of the Isaac Newton Institute Seminar Series series.

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