COLLECTED WORKS OF JOHN TATE – Part I and II

Editores: Barry Mazur (Harvard University, Cambridge, MA,USA), Jean-Pierre Serre (Collège de France, París, Francia)

Providence, RI, USA. AMERICAN MATHEMATICAL SOCIETY. ISBN: 9780821890912.  1.414 págs. Enero de 2017. Encuadernado

PVP EUR 312,00 (4% IVA incluido)                   

Les ofrecemos el volumen 24 de la serie COLLECTED WORKS. Podemos enviarles más información sobre otros volúmenes, si así lo desean.

En estos volúmenes encontraremos todos los artículos matemáticos publicados por John Tate, que abarcan más de seis décadas, enriquecidos por los nuevos comentarios hechos por el autor. Se incluye también una selección de sus cartas, las cuales nos dan una visión cercana de cómo trabaja y de sus ideas en proceso de formación.

 

Pueden adquirirse por separado – Part I. ISBN: 9780821890929 – Part II. ISBN: 9780821890936, con un precio de EUR 187,00 (4% IVA incluido), cada parte.

Extracto del índice:

Part I

-Photo section

-Contents

-Foreword

-Preface

-Permissions and acknowledgments

-Curriculum vitae

-List of former students

1. Fourier analysis in number fields and Hecke’s zeta-functions

2. A note on finite ring extensions

3. On the relation between extremal points of convex sets and homomorphisms of algebras

4. Genus change in inseparable extensions of function fields

5. On Chevalley’s proof of Luroth’s theorem

6. The higher dimensional cohomology groups of class field theory

7. The cohomology groups of algebraic number fields

8. On the Galois cohomology of unramified extensions of function fields in one variable

9. On the characters of finite groups

10. Homology of Noetherian rings and local rings

11. WC-groups over -adic fields

12. On the inequality of Castelnuovo-Severi

13. On the inequality of Castelnuovo-Severi, and Hodge’s theorem

14. Principal homogeneous spaces for abelian varieties

15. Principal homogeneous spaces over abelian varieties

16. A different with an odd class

17. Nilpotent quotient groups

18. Duality theorems in Galois cohomology over number fields

19. Ramification groups of local fields

20. Formal complex multiplication in local fields

21. Algebraic cycles and poles of zeta functions

22. Elliptic curves and formal groups

23. On the conjectures of Birch and Swinnerton-Dyer and a geometric analog

24. Formal moduli for one-parameter formal Lie groups

25. The cohomology groups of tori in finite Galois extensions of number fields

26. Global class field theory

27. Endomorphisms of abelian varieties over finite fields

28. The rank of elliptic curves

29. Residues of differentials on curves

30. -Divisible groups

31. The work of David Mumford

32. Classes d’isogénie des variétés abéliennes sur un corps fini (d’après T. Honda)

33. Good reduction of abelian varieties

34. Group schemes of prime order

35. Symbols in arithmetic

36. Rigid analytic spaces

37. The Milnor ring of a global field

38. Appendix to “The Milnor Ring of a global field”

39. Letter from Tate to Iwasawa on a relation between ₂ and Galois cohomology

40. Points of order 13 on elliptic curves

41. The arithmetic of elliptic curves

42. The 1974 Fields Medals (I): An algebraic geometer

43. Algorithm for determining the type of a singular fiber in an elliptic pencil

-Letters (to Serre; Dwork, Springer, Birch and Atkins)

Part II

-Photos

-Contents

-Foreword

-Preface

-Permissions and acknowledgments

-Curriculum vitae

-List of former students

44. Problem 9: The general reciprocity law

45. Relations between ₂ and Galois cohomology

46. Local constants

47. On the torsion in ₂ of fields

48. Fields medals (IV): An instinct for the key idea

49. A simple proof of the main theorem of elimination theory in algebraic geometry

50. Number theoretic background

51. The Harish-Satake transform on ᵣ

52. Brumer-Stark-Stickelberger

53. On conjugation of abelian varieties of CM type

54. On Stark’s conjectures on the behavior of (,) at =0

55. Variation of the canonical height of a point depending on a parameter

56. A reciprocity law for ₂-traces

57. Canonical height pairings via biextensions

58. On -adic analogues of the conjectures of Birch and Swinnerton-Dyer

59. Refined conjectures of the “Birch and Swinnerton-Dyer type”

60. Commentary on algebra

61. Some algebras associated to automorphisms of elliptic curves

62. The -adic sigma function

63. Quantum deformations of _{}

64. Modules over regular algebras of dimension 3

65. Conjectures on algebraic cycles in ℓ-adic cohomology

66. The center of the 3-dimensional and 4-dimensional Sklyanin algebras

67. The non-existence of certain Galois extensions of ℚ unramified outside

68. The centers of 3-dimensional Sklyanin algebras

69. A review of non-Archimedean elliptic functions

70. Homological properties of Sklyanin algebras

71. Linear forms in -adic roots of unity

72. Finite flat group schemes

73. Bernard Dwork (1923-1998)

74. Galois cohomology

75. On a conjecture of Finotti

76. Refining Gross’s conjecture on the values of abelian -functions

77. On the Jacobians of plane cubics

78. Computation of -adic heights and log convergence

-Letters (to Serre)

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