Аннотация:
In this series of talks we will give an introduction to a method discovered by Minhyong Kim. The method uses prounipotent completion of the fundamental Poincare groupoid with (rational) $p$-adic Hodge theory and allows to obtain upper bounds on integral points on arithmetic varieties. In particular, the method provides a proof of the Mordell conjecture in a number of cases.
In the first talk we will give an overview of this method, considering it as a generalization of the method of Chabauty and Coleman. Also, we will start giving a general introduction to $p$-adic Hodge theory. No special prerequisites are required.
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