Bibliography: J.S. Milne (October 24, 2004).

Items marked * are not available at http://www.jmilne.org/math/

Articles

  1. Extensions of abelian varieties defined over a finite field , Invent. Math. 5 (1968), 63-84.
  2. The Tate-\v Safarevi\v c group of a constant abelian variety , Invent. Math. 6 (1968), 91-105.
  3. The homological dimension of commutative group schemes over a perfect field, J. Algebra 16 (1970), 436-441.
  4. Weil-Châtelet groups over local fields, Ann. Sci. Ecole Norm. Sup. 4 series, T3 (1970), 273-284.
  5. Elements of order p in the Tate-\v Safarevi\v c group, Bull. London Math. Soc. 2 (1970), 293-296.
  6. The Brauer group of a rational surface, Invent. Math. 11 (1970), 304-307.
  7. Abelian varieties over finite fields, Proc. Symp. Pure Math. 20 (1971), 53-64. (with W. C. Waterhouse).
  8. Weil-Châtelet groups over local fields, Addendum, Ann. Sci. Ecole Norm. Sup. T5 (1972), 261-264.
  9. On the arithmetic of abelian varieties , Invent. Math. 17 (1972), 177-190.
  10. Congruence subgroups of abelian varieties , Bull. Sci. Math. 96 (1972), 333-338.
  11. Abelian varieties defined over their fields of moduli , I, Bull. London Math. Soc. 4 (1972), 370-372.
  12. On a theorem of Mazur and Roberts , Amer. J. Math. 95 (1973), 80-86.
  13. On a conjecture of Artin and Tate , Annals of Math. 102 (1975), 517-533.
  14. Duality in the flat cohomology of curves , Invent. Math. 35 (1976), 111-129 (with M. Artin).
  15. Flat homology , Bull. Amer. Math. Soc. 82 (1976), 118-120.
  16. Duality in the flat cohomology of surfaces , Ann. Sci. Ecole Norm. Sup. 9 (1976), 171-202.
  17. Points on Shimura varieties mod p , Proc. Symp. Pure Math. 33 (1979), part 2, 165-184.
  18. Etude d'une class d'isogénie, in Variétiés de Shimura et Fonctions L, Publications Mathématiques de l'Université Paris 7 (1979), 73-81.
  19. Some estimates from étale cohomology, J. Reine Angew. Math. 328 (1981), 208-220.
  20. The action of complex conjugation on a Shimura variety, Annals of Math. 113 (1981), 569-599. (with K-y. Shih).
  21. Automorphism groups of Shimura varieties and reciprocity laws , Amer. J. Math. 103 (1981), 1159-1175. (with K-y. Shih).
  22. Hodge cycles and abelian varieties (notes of a seminar of P. Deligne), in Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Math. 900 (1982), Springer, Heidelberg, 9-100.
  23. Tannakian categories , in Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Math. 900 (1982), Springer, Heidelberg, 101-228. (with P. Deligne).
  24. Langlands's construction of the Taniyama group , in Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Math. 900 (1982), Springer, Heidelberg, 229-260. (with K-y. Shih).
  25. Conjugates of Shimura varieties , in Hodge Cycles, Motives, and Shimura Varieties, Lecture Notes in Math. 900 (1982), Springer, Heidelberg, 280-356. (with K-y. Shih).
  26. Zero cycles on algebraic varieties in nonzero characteristic: Rojtman's theorem , Compositio Math. 47 (1982), 271-287.
  27. Comparison of the Brauer group with the Tate-\v Safarevi\v c group , J. Fac. Sci. Univ. Tokyo (Shintani Memorial Volume) IA 28 (1982), 735-743.
  28. The action of an automorphism of C on a Shimura variety and its special points, In Arithmetic and Geometry, Papers dedicated to I.R. Shafarevich on the occasion of his sixtieth birthday, Progress in Math. 35 (1983), Birkhauser Verlag, 239-265.
  29. Values of zeta functions of varieties over finite fields, Amer. J. Math. 108, (1986), 297-360.
  30. Abelian varieties , in Arithmetic Geometry (Proc. Conference on Arithmetic Geometry, Storrs, August 1984) Springer, 1986, 103-150.
  31. Jacobian varieties , Ibid., 167-212.
  32. Automorphic vector bundles on connected Shimura varieties , Inventiones math., 92 (1988), 91-128.
  33. Motivic cohomology and values of zeta functions , Compos. math. 68 (1988), 59-102.
  34. Canonical models of (mixed) Shimura varieties and automorphic vector bundles . In Automorphic Forms, Shimura Varieties, and L-Functions (Proceedings of a Conference held at the University of Michigan, Ann Arbor, July 6-16, 1988), Perspectives in Mathematics Vols 10, 11, Academic Press, 1990, pp 283-414.
  35. The conjecture of Langlands and Rapoport for Siegel modular varieties . Bull. AMS, 24 (1991), 335-341.
  36. The points on a Shimura variety modulo a prime of good reduction. In: The Zeta Function of Picard Modular Surfaces, Publ. Centre de Rech. Math., Montreal (Eds. R. Langlands and D. Ramakrishnan), 1992, pp151--253.
  37. Motives over finite fields. In: Motives (Eds. U. Jannsen, S. Kleiman, J.-P. Serre), AMS, Proc. Symp Pure Math. 55, 1994, Part 1, pp401--459.
  38. Shimura varieties and motives. In: Motives (Eds. U. Jannsen, S. Kleiman, J.-P. Serre), Proc. Symp. Pure Math., AMS, 55, 1994, Part 2, pp447--523.
  39. Shimura variety,In: Encyclopaedia of Mathematics Supplement Volume I (Editor-in-Chief M. Hazewinkel), Kluwer Acad. Publ., 1997, pp448--449.
  40. Lefschetz classes on abelian varieties , Duke Math. J. 96 (1999), pp. 639-675.
  41. Lefschetz motives and the Tate conjecture , Compositio Math. 117 (1999), pp. 47-81.
  42. Descent for Shimura varieties. Michigan Math. J., 46 (1999), pp.203--208.
  43. The Tate conjecture for certain abelian varieties over finite fields. Acta Arith. 100 (2001), no. 2, pp.135--166.
  44. Polarizations and Grothendieck's standard conjectures, Ann. of Math. 155 (2002), pp. 599--610.
  45. Gerbes and abelian motives 2003, eprint, arXiv:math.AG/0301304, 42 pages.
  46. Integral motives and special values of zeta functions With Niranjan Ramachandran. J. Amer. Math. Soc. 17 (2004), 499-555.
  47. Periods of abelian varieties Compositio Math. 140 (2004), 1149--1175.
  48. Introduction to Shimura varieties Preprint 130pp; To appear in the book of the Clay Mathematics Institute Summer School on Harmonic Analysis, The Trace Formula and Shimura Varieties, held at the Fields Institute, June 2 -- June 27, 2003.
  49. The de Rham-Witt and Zp-cohomologies of an algebraic variety (with Niranjan Ramachandran) Preprint, submitted.
  50. Various papers in preparation.

Books

  1. Etale Cohomology, Princeton Univ. Press (1980), 323pp. (Second printing 1980, Russian translation 1982, Third printing 1991).
  2. Hodge Cycles, Motives, and Shimura Varieties , Lecture Notes in Math. 900 (1982), Springer, Heidelberg, 414 pp. (with P. Deligne, A. Ogus and Kuang-yen Shih). (Russian translation 1985.) (Reprinted with additional material 1989.)
  3. Arithmetic Duality Theorems , Perspectives in Mathematics, No. 1, Academic Press, 1986, 432pp.
  4. Automorphic Forms, Shimura Varieties, and L-Functions, (Proceedings of a Conference held at the University of Michigan, Ann Arbor, July 6-16, 1988), Perspectives in Mathematics Vols 10, 11, Academic Press, 1990. (Editor, with L. Clozel)

Course Notes

  1. Group Theory; Fields and Galois Theory
  2. Algebraic Geometry
  3. Algebraic Number Theory
  4. Modular Functions and Modular Forms
  5. Elliptic Curves
  6. Abelian Varieties
  7. Lectures on Etale Cohomology
  8. Class Field Theory

Other Manuscripts

  1. The conjectures of Birch and Swinnerton-Dyer for constant abelian varieties over function fields, 75pp, May 1967. Thesis, published in improved form as articles [1] and [2].
  2. Shimura varieties: conjugates and the action of complex multiplication . 154pp, October 1979 (with K-y. Shih). Published as articles [20], [24], and [25].
  3. Abelian varieties with complex multiplication (for pedestrians), 42pp, September 19, 1981. (Added footnotes and an appendix, and placed it on the web June 7, 1998.)
  4. Kazhdan's theorem on arithmetic varieties. 42pp, March 28, 1984.
  5. *The conjecture of Langlands and Rapoport for Siegel modular varieties, 60pp, March 13, 1990. (The details for article [35].)
  6. Shimura Varieties: The geometric side of the zeta function. (Notes for talks at IAS, Feb 21,23,28, March 2, 1995)
  7. Canonical models of Shimura curves
  8. The (failure of the) Hasse principle for centres of semisimple groups