James Milne (mathematician)

James S. Milne (born October 10, 1942 in Invercargill, New Zealand) is a New Zealand mathematician working in arithmetic geometry.

Milne attended the High School in Invercargill in New Zealand until 1959, and then studied at the University of Otago in Dunedin (BA 1964) and 1964 to 1967 at Harvard University (Masters 1966), where in 1967 under the supervision of John Tate he received his doctorate. He was then to 1969 a lecturer at University College London and from 1969 he is at the University of Michigan, first as Assistant Professor, from 1972 as Associate Professor in 1977 and finally as a professor. Since 2000 he has been Professor Emeritus. He was a visiting professor at King's College in London, at the IHES in Paris (1975, 1978), at the MSRI, Berkeley (1986–87) and the Institute for Advanced Study in Princeton (1976–77, 1982, 1988).

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 characteristic not equal to zero. He also gave the first example of abelian varieties with finite Tate–Shafarevich group. He then went to study Shimura varieties (certain hermitian symmetric spaces, low-dimensional examples being modular curves) and motives.

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.

• Étale Cohomology, Princeton University Press, 1980
• Abelian Varieties, Jacobean Varieties, in Arithmetic Geometry Proc.Conference Storrs 1984, Springer 1986
• With Pierre Deligne, Arthur Ogus, Kuang-yen Shih, Hodge Cycles, Motives and Shimura Varieties, Springer Verlag, Lecture Notes in Mathematics Bd.900, 1982 (therein by Deligne: Tannakian Categories)
• Arithmetic Duality Theorems, Academic Press, Perspectives in Mathematics, 1986
• Editor with Laurent Clozel, Automorphic Forms, Shimura Varieties and L-Functions, 2 volumes, Elsevier 1988 (Conference University of Michigan, 1988)
• Elliptic Curves, BookSurge Publishing 2006
• Shimura Varieties and Motives in Jannsen, Kleiman, Serre (editor) motif, Proc.Symp.Pure Bd.55 Math, AMS, 1994

• Bloch, Spencer (1981). "Review: Étale cohomology by J. S. Milne" (PDF). Bull. Amer. Math. Soc. (N.S.). 4 (2): 235–239. doi:10.1090/s0273-0979-1981-14894-1.