James Milne (mathematician)

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

Milne attended by 1959 high school in Invercargill in New Zealand, then studied at the University of Otago in Dunedin (Bachelor 1964) and from 1964 to 1967 at Harvard University (Master 1966), where he earned his doctorate under John T. Tate 1967. After that, he was until 1969 Lecturer at University College London and finally worked from 1969 at the University of Michigan, first as an assistant professor, in 1972 as an associate professor and from 1977 as a professor. Since 2000 he is a professor emeritus. He was a visiting professor at, among others, King's College, London, at the IHES in Paris (1975, 1978), at the 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 conjecture of Birch and Swinnerton - Dyer for constant abelian varieties over function fields in characteristic not equal to zero ( Inventiones Mathematicae Bd.6, 1986 p.91). He was also the first examples of abelian varieties with finite Tate - Shafarevich group. He continued to struggle with, among other Shimura varieties ( special Hermitian symmetric spaces, examples of lower dimension are modular curves) and motifs.

His doctoral counts Pyotr Blass.

Milne is a passionate mountaineer.

Writings

  • Etale 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 with Deligne: Tannakian Categories)
  • Arithmetic Duality Theorem, Academic Press, Perspectives in Mathematics, 1986
  • Publisher 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 Math Bd.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
John Tate Birch and Swinnerton-Dyer conjecture Characteristic (algebra) Mathematics Genealogy Project
428065
de