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Hardcover ISBN:  9780821890929 
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Hardcover ISBN:  9780821890929 
Product Code:  CWORKS/24.1 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
eBook ISBN:  9781470430214 
Product Code:  CWORKS/24.1.E 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
Hardcover ISBN:  9780821890929 
eBook ISBN:  9781470430214 
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 DetailsCollected WorksVolume: 24; 2016; 716 ppMSC: 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.
ReadershipGraduate 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 zetafunctions

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. WCgroups over 𝔭adic fields

12. On the inequality of CastelnuovoSeveri

13. On the inequality of CastelnuovoSeveri, 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 SwinnertonDyer and a geometric analog

24. Formal moduli for oneparameter 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. 𝑝Divisible 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. 𝔭adic 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


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
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.
Graduate students and research mathematicians interested in algebraic geometry and number theory.

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 zetafunctions

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. WCgroups over 𝔭adic fields

12. On the inequality of CastelnuovoSeveri

13. On the inequality of CastelnuovoSeveri, 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 SwinnertonDyer and a geometric analog

24. Formal moduli for oneparameter 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. 𝑝Divisible 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. 𝔭adic 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