p-adic unlikely intersections and rational points on curves

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• Netan Dogra (University of Oxford)
• Tuesday 14 May 2019, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jack Thorne.

Chabauty’s method aims to find rational points on a higher genus curve by exploiting the fact that their p-adic logarithms satisfy non-trivial identities. When applying this method over number fields, one encounters the problem of proving that the set of p-adic points satsifying these identities is finite, or equivalently of ruling out the existence of ‘unlikely intersections’ between the different zero sets. In this talk I will describe how ideas in functional transcendence can be used to understand this problem, and its non-abelian generalisation due to Kim.

This talk is part of the Number Theory Seminar series.

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