004 The Uniform Mordell-Lang Problem

2021-09-11 13:48:06



1.时间安排:9月25日 09:00-10:20


报告题目:Basic height theory

报告摘要:The goal is to introduce Weil's height machine, Neron-Tate height of abelian varieties, and the application to the Mordell-Weil theorem.

2.时间安排:9月25日 10:30-11:50


报告题目:Basic Arakelov theory

报告摘要:This lecture introduces arithmetic divisors and hermitian line bundles over arithmetic varieties, and defines their top intersection numbers. Define height functions associated to hermitian line bundles. Introduce ampleness, bigness, nefness of hermitian line bundles.

3.时间安排:9月25日 13:30-14:30


报告题目:Basics on the moduli spaces of curves

报告摘要:This is a review of the definition and GIT construction of the moduli spaces of smooth curves and stable curves. Introduce the tautological divisors (Hodge bundle, boundary divisors) over the moduli space of stable curves. Introduce Noether's formula.

4.时间安排:9月25日 14:40-15:40


报告题目:Introduction to the Mordell conjecture

报告摘要:This is an overview of the proofs of the Mordell conjecture, with some details on Vojta's proof (simplified by Faltings, Bombieri).

5.时间安排:9月25日 16:10-17:10


报告题目:Introduction to Berkovich spaces

报告摘要:This is an outline of the theory of Berkovich analytic spaces. It will also cover metrized line bundles, and Green's functions over Berkovich spaces.

6.时间安排:9月25日 17:20-18:20


报告题目:Introduction to the Bogomolov conjecture

报告摘要:This is an introduction to various forms of the Bogomolov conjecture, with some details on the lower bound of ωa2 for curves in terms of the φ-invariant following Zhang, Cinkir, de Jong.

7.时间安排:9月26日 9:00-11:50


报告题目:Uniform Mordell-Lang and uniform Bogomolov I,II

报告摘要:This is an introduction to the recent results on the uniform Mordell-Lang problem and the uniform Bogomolov problem of Dimitrov-Habegger-Gao, Kühne and Yuan. We will focus on Yuan's approach.