Collected Works of John Tate - Parts I and II: 1951-2006

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. 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 -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