James Milne

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James S. Milne (born October 10, 1942 in Invercargill , New Zealand ) is a New Zealand mathematician who deals with arithmetic geometry , the interface between number theory and algebraic geometry .

Milne attended high school in Invercargill in New Zealand until 1959 , then studied at the University of Otago in Dunedin (Bachelor 1964) and from 1964 to 1967 at Harvard University (Master 1966), where he received his doctorate in 1967 under John T. Tate . Then he was a lecturer at University College London until 1969 and worked at the University of Michigan from 1969 , first as an assistant professor, from 1972 as an associate professor and from 1977 finally as a professor. Since 2000 he has been Professor Emeritus there. He was visiting professor at King's College in London, at IHÉS near Paris (1975, 1978), at MSRI in Berkeley (1986/87) and at 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 Birch and Swinnerton-Dyer conjecture for constant Abelian varieties over function fields with characteristic non-zero ( Inventiones Mathematicae Vol. 6, 1986, P. 91). There he also gave the first examples of Abelian varieties with finite Tate Shafarevich groups . He also dealt with Shimura varieties (special Hermitian symmetrical spaces, examples of low dimensions are modular curves ) and motifs .

Pyotr Blass is one of his doctoral students.

Milne is a passionate mountaineer.


  • Etale Cohomology , Princeton University Press 1980
  • Abelian Varieties , Jacobean Varieties , in Proc. Conference Arithmetic Geometry Storrs 1984, Springer 1986
  • with Pierre Deligne , Arthur Ogus, Kuang-Yen Shih Hodge Cycles, Motives and Shimura Varieties , Springer Verlag, Lecture Notes in Mathematics Vol. 900, 1982 (in it with 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) Motives , Proc.Symp.Pure Math. Vol. 55, AMS, 1994
  • What is a Shimura Variety? , Notices AMS, December 2012, online
  • Introduction to Shimura Varieties , Clay Math. Proc., Volume 4, 2005, American Mathematical Society, pp. 265-378

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