MA 254 0 Number Theory II
Spring 2015-16

Instructor: Dan Abramovich
Class meeting: Mondays, Wednesdays and Fridays at 1:00-1:50am in Kassar 105
Office: Kassar 118
Telephone: (401) 863 7968
E-mail: abrmovic ( at ) math (period) brown (dot) edu
Web site:
Canvas: direct link
Preliminary Office hours: Wednesday, 2:00-3:00, Monday and Friday 10:00-10:50

Text: Diophantine Geometry by Hindry and Silverman, Springer GTM.
Topics: Heights; The Mordell-Weil theorem; The theorems of Roth and Siegel; Proof of Mordell's conjecture - Bombieri's combined approach.
I'll follow the outline on page 369, except I won't cover Part A.

Course requirements
Homework will be assigned regularly from the book.
Students are required to organize and run a study group Algebraic geometry for number theorists, following Part A, supplemented by Hartshorne's Algebraic geometry, especially chapter 4, Mumford's Abelian varieties, especially Chapters 1-3, and Cornell-Silverman's Arithmetic Geometry, chapters on abelian varieties and Jacobian varieties by Rosen and Milne.

Comments on the book by us, and Corrections and comments on the book by the authors

Absolute values
Heights on projective spaces
Heights on varieties
Canonical Heights
D.1: Dirichlet and Liouville (by C. Frechette)
The S-unit equation
Faltings's theorem (Mordell's conjecture)

Presentation lineup
Hermite's Theorems: Zhou Fang
Section D.1: Claire Frechette (presented March 4)
Section D.2: David Lowrie (March 7)
Section D.3: Thomas Silverman, Laura Walton
Section D.4: Dori Bejleri, Alicia Harper
Section D.5: Giovanny Inchiostro and Kenneth Ascher
Section D.6: Shamil Asgarli and Yuwei Zhu
Section D.7: Seoyoung Kim

First assignment (evolving): Exercises B2, B3, B4,