James Milne (mathematician)


James S. Milne is a New Zealand mathematician working in arithmetic geometry.

Life

Milne attended high school in Invercargill in New Zealand until 1959, and then studied at the University of Otago in Dunedin and Harvard University. From then to 1969 he was a lecturer at University College London. After that he was at the University of Michigan, as Assistant Professor, Associate Professor, Professor, and Professor Emeritus. He has also been a visiting professor at King's College London, at the Institut des hautes études scientifiques in Paris, at the Mathematical Sciences Research Institute in Berkeley, California, and the Institute for Advanced Study in Princeton, New Jersey.
In his dissertation, entitled "The conjectures of Birch and Swinnerton-Dyer for constant abelian varieties over function fields," he proved the conjecture of Birch and Swinnerton–Dyer for constant abelian varieties over function fields in one variable over a finite field. He also gave the first examples of nonzero abelian varieties with finite Tate–Shafarevich group. He went on to study Shimura varieties and motives.
For 2025 Milne was awarded the Leroy P. Steele Prize for Mathematical Exposition of the American Mathematical Society.
His students include Piotr Blass, Michael Bester, Matthew DeLong, Pierre Giguere, William Hawkins Jr, Matthias Pfau, Victor Scharaschkin, Stefan Treatman, Anthony Vazzana, and Wafa Wei.
Milne is also an avid mountain climber.

Writings

Abelian Varieties, Jacobian Varieties, in Arithmetic Geometry Proc. Conference Storrs 1984, Springer 1986