Height Study Seminar
I’m organizing a study seminar on the theory of heights, based on the book Heights in Diophantine Geometry.
We will be focusing on three results: Mordell-Weil theorem, Falting theorem, and potentially Vojta conjecture. If time permits, we will also try to cover Manin’s conjecture for toric varieties. We will start slow and spend one or two talks on naive heights on projective space. Then we will define Weil heights for projective varieties, and study their properties. After this, we will focus on abelian varieties, and once we are familar with those objects, we introduce Neron-Tate heights, and finally prove the first main result we want to cover (actually, I think this will be all we can do this term (spring 2024)).
Talk 1: Introduction to Naive Heights (2024-05-20)
Speaker: Cynthia Dai
In this talk, we will review some number theory, then present the definition of heights for projective space.
Talk 2: Local Heights (2024-05-27)
Speaker: Cynthia Dai
In this talk, we will wrap up heights on projective space by prove Northcott’s theorem for algebraic numbers. Next, we will local heights with respect to a Cartier divisor.
Talk 3: Global Heights (2024-06-03)
Speaker: Cynthia Dai
In this talk, we finished local heights and defined global heights, then finished with explicit bound on the difference for Weil height.
Talk 4: Group Varieties (2024-06-03)
Speaker: Cynthia Dai
In this talk, we will define and study basic property of group varieties.