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Collected Works of John Tate: Part I (1951–1975)
 
John Tate Harvard University, Cambridge, MA
Edited by: Barry Mazur Harvard University, Cambridge, MA
John Tate University of Texas, Austin, TX
Jean-Pierre Serre Collège de France, Paris, France
Collected Works of John Tate
Hardcover ISBN:  978-0-8218-9092-9
Product Code:  CWORKS/24.1
List Price: $175.00
MAA Member Price: $157.50
AMS Member Price: $140.00
eBook ISBN:  978-1-4704-3021-4
Product Code:  CWORKS/24.1.E
List Price: $175.00
MAA Member Price: $157.50
AMS Member Price: $140.00
Hardcover ISBN:  978-0-8218-9092-9
eBook: ISBN:  978-1-4704-3021-4
Product Code:  CWORKS/24.1.B
List Price: $350.00 $262.50
MAA Member Price: $315.00 $236.25
AMS Member Price: $280.00 $210.00
Collected Works of John Tate
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Collected Works of John Tate: Part I (1951–1975)
John Tate Harvard University, Cambridge, MA
Edited by: Barry Mazur Harvard University, Cambridge, MA
John Tate University of Texas, Austin, TX
Jean-Pierre Serre Collège de France, Paris, France
Hardcover ISBN:  978-0-8218-9092-9
Product Code:  CWORKS/24.1
List Price: $175.00
MAA Member Price: $157.50
AMS Member Price: $140.00
eBook ISBN:  978-1-4704-3021-4
Product Code:  CWORKS/24.1.E
List Price: $175.00
MAA Member Price: $157.50
AMS Member Price: $140.00
Hardcover ISBN:  978-0-8218-9092-9
eBook ISBN:  978-1-4704-3021-4
Product Code:  CWORKS/24.1.B
List Price: $350.00 $262.50
MAA Member Price: $315.00 $236.25
AMS Member Price: $280.00 $210.00
  • Book Details
     
     
    Collected Works
    Volume: 242016; 716 pp
    MSC: Primary 01; 11; 14

    In these volumes, a reader will find all of John Tate's published mathematical papers—spanning more than six decades—enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.

    Readership

    Graduate students and research mathematicians interested in algebraic geometry and number theory.

    This item is also available as part of a set:
  • Table of Contents
     
     
    • Cover
    • Title page
    • 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 𝔭-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. 𝑝-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 𝐾₂ 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
    • L1. Letter to Dwork (1958/2/13)
    • L2. 𝔭-adic elliptic functions and the Tate curve (letter to Serre, 1959/8/4)
    • L3. Galois cohomology of finite modules and abelian varieties (letter to Serre, 1962/6/18)
    • L4. Euler characteristic of finite Galois modules over local fields (letter to Serre, 1963/4/7)
    • L5. Weird duality (letter to Serre, 1963/4/17)
    • L6. Hom and Ext (letter to Serre, 1963/4/23)
    • L7. Letter to Serre (1963/4/25)
    • L8. Letter to Serre (1964/1/10)
    • L9. Letter to Serre (1965/1/12)
    • L10. Letter to Serre (1965/5/21)
    • L11. Letter to Springer (1966/1/13)
    • L12. Letter to Serre (1968/6/21)
    • L13. Letter to Dwork (1968/11/15)
    • L14. Letter to Birch (1969/3/19)
    • L15. Letter to Serre (1971/7/22)
    • L16. Letter to Serre (1974/3/26)
    • L17. Letter to Serre (1974/5/2)
    • L18. Letter to Atkin (1974/6/18)
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     
    • These volumes contain a treasure trove of beautiful and important results, now collected in one place for the edification and delight of present and future generations of mathematicians.

      Michael I. Rosen, Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 242016; 716 pp
MSC: Primary 01; 11; 14

In these volumes, a reader will find all of John Tate's published mathematical papers—spanning more than six decades—enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.

Readership

Graduate students and research mathematicians interested in algebraic geometry and number theory.

This item is also available as part of a set:
  • Cover
  • Title page
  • 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 𝔭-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. 𝑝-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 𝐾₂ 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
  • L1. Letter to Dwork (1958/2/13)
  • L2. 𝔭-adic elliptic functions and the Tate curve (letter to Serre, 1959/8/4)
  • L3. Galois cohomology of finite modules and abelian varieties (letter to Serre, 1962/6/18)
  • L4. Euler characteristic of finite Galois modules over local fields (letter to Serre, 1963/4/7)
  • L5. Weird duality (letter to Serre, 1963/4/17)
  • L6. Hom and Ext (letter to Serre, 1963/4/23)
  • L7. Letter to Serre (1963/4/25)
  • L8. Letter to Serre (1964/1/10)
  • L9. Letter to Serre (1965/1/12)
  • L10. Letter to Serre (1965/5/21)
  • L11. Letter to Springer (1966/1/13)
  • L12. Letter to Serre (1968/6/21)
  • L13. Letter to Dwork (1968/11/15)
  • L14. Letter to Birch (1969/3/19)
  • L15. Letter to Serre (1971/7/22)
  • L16. Letter to Serre (1974/3/26)
  • L17. Letter to Serre (1974/5/2)
  • L18. Letter to Atkin (1974/6/18)
  • Back Cover
  • These volumes contain a treasure trove of beautiful and important results, now collected in one place for the edification and delight of present and future generations of mathematicians.

    Michael I. Rosen, Mathematical Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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