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An Effective Generalization of Liouville`s Theorem for Projective Varieties

Speaker

Francois Ballay, Beijing International Center for Mathematical Research (BICMR) Peking University. Beijing.

Time

2018.06.13 14:00-15:00

Venue

Middle Lecture Room, Math Building

Abstract

The fundamental problem in Diophantine approximation is to know how closely an irrational number can be approximated by a rational number. I will describe how this question can be generalized to the case of closed points on a projective variety defined over a number field. In particular, I will present an effective Liouville type Theorem, which gives an explicit upper bound for the height of rational points that are close to a given algebraic point of the variety. The main result is an effective version of a recent Theorem of David McKinnon and Mike Roth, which highlights Diophantine properties of Seshadri constants.