Research-Counting rational points in arithmetic varieties by determinant method

Research

Algebra & Combinatorics Seminar

Counting rational points in arithmetic varieties by determinant method

Speaker: LIU Chunhui (Universite Paris 7)
Time: Aug 15, 2017, 16:10-17:10
Location: Conference Room 415, Wisdom Valley 3#

By the slope method in Arakelov geometry, we can construct a family of hypersurfaces which cover the rational points of bounded height on an arithmetic variety but don't contain the generic point of this variety. By estimating some invariants of Arakelov geometry, we can control the number and the maximal degree of this family of auxiliary hypersurfaces explicitly. In this talk, I will explain the method of studying the problem of counting rational points by the approach of Arakelov geometry.