A celebrated result of Coleman gives a completely explicit version of Chabauty’s finiteness theorem for rational points in hyperbolic curves over a number field, by a study of zeros of p-adic analytic functions. After several developments around this result, the problem of proving an analogous explicit bound for higher dimensional subvarieties of abelian varieties remains elusive. In this talk I’ll sketch the proof of such a bound for hyperbolic surfaces contained in abelian threefolds.
This is joint work with Jerson Caro.
This video is part of the Number Theory Web Seminar series.
