北京雁栖湖应用数学研究院

In 1980s, Faltings proved the Mordell conjecture which states that any smooth projective curve over a number field of genus greater than 1 has only finitely many rational points. In this course, we will go over a different proof recently given by Lawrence and Venkatesh using p-adic Hodge theory; they consider a p-adic period map which encodes the variation of p-adic Galois representations in a family of algebraic varieties, and study its relation to the complex period map. We will also discuss their application of the method to higher dimensional situations.