Overview

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.

Full Product Details

Author:   Barry Mazur ,  Jean-Pierre Serre
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   3.121kg
ISBN:  

9780821890912

ISBN 10:   0821890913
Pages:   1414
Publication Date:   30 December 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Part I: Fourier analysis in number fields and Hecke's zeta-functions by J. T. Tate A note on finite ring extensions by E. Artin and J. T. Tate On the relation between extremal points of convex sets and homomorphisms of algebras by J. Tate Genus change in inseparable extensions of function fields by J. Tate On Chevalley's proof of Luroth's theorem by S. Lang and J. Tate The higher dimensional cohomology groups of class field theory by J. Tate The cohomology groups of algebraic number fields by J. T. Tate On the Galois cohomology of unramified extensions of function fields in one variable by Y. Kawada and J. Tate On the characters of finite groups by R. Brauer and J. Tate Homology of Noetherian rings and local rings by J. Tate WC-groups over $p$-adic fields by J. Tate On the inequality of Castelnuovo-Severi by E. Artin and J. Tate On the inequality of Castelnuovo-Severi, and Hodge's theorem by J. Tate Principal homogeneous spaces over abelian varieties by S. Lang and J. Tate Principal homogeneous spaces for abelian varieties by J. Tate A different with an odd class by A. Frohlich, J.-P. Serre, and J. Tate Nilpotent quotient groups by J. Tate Duality theorems in Galois cohomology over number fields by J. Tate Ramification groups of local fields by S. Sen and J. Tate Formal complex multiplication in local fields by J. Lubin and J. Tate Algebraic cycles and poles of zeta functions by J. T. Tate Elliptic curves and formal groups by J. Lubin, J. Serre, and J. Tate On the conjectures of Birch and Swinnerton-Dyer and a geometric analog by J. Tate Formal moduli for one-parameter formal Lie groups by J. Lubin and J. Tate The cohomology groups of tori in finite Galois extensions of number fields by J. Tate Global class field theory by J. T. Tate Endomorphisms of abelian varieties over finite fields by J. Tate The rank of elliptic curves by J. T. Tate and I. R. Safarevic Residues of differentials on curves by J. Tate $p$-divisible groups by J. T. Tate The work of David Mumford by J. Tate Classes d'isogenie des varietes abeliennes sur un corps fini (d'apres T. Honda) by J. Tate Good reduction of abelian varieties by J.-P. Serre and J. Tate Group schemes of prime order by J. Tate and F. Oort Symbols in arithmetic by J. Tate Rigid analytic spaces by J. Tate The Milnor ring of a global field by H. Bass and J. Tate Appendix by H. Bass and J. Tate Letter from Tate to Iwasawa on a relation between $K_2$ and Galois cohomology by J. Tate Points of order 13 on elliptic curves by B. Mazur and J. Tate The arithmetic of elliptic curves by J. T. Tate The 1974 Fields Medals (I): An algebraic geometer by J. Tate Algorithm for determining the type of a singular fiber in an elliptic pencil by J. Tate Letters by J. Tate Part II: Problem 9: The general reciprocity law by J. Tate Relations between $K_2$ and Galois cohomology by J. Tate Local constants by J. T. Tate On the torsion in $K_2$ of fields by J. Tate Fields medals (IV): An instinct for the key idea by J. Tate A simple proof of the main theorem of elimination theory in algebraic geometry by P. Cartier and J. Tate Number theoretic background by J. Tate The Harish-Satake transform on $GL_r$ by J. Tate Brumer-Stark-Stickelberger by J. Tate On conjugation of abelian varieties of CM type by J. Tate On Stark's conjectures on the behavior of $L(s,\chi)$ at $s=0$ by J. Tate Variation of the canonical height of a point depending on a parameter by J. Tate A reciprocity law for $K_2$-traces by S. Rosset and J. Tate Canonical height pairings via Biextensions by B. Mazur and J. Tate On $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer by B. Mazur, J. Tate, and J. Teitelbaum Refined conjectures of the ``Birch and Swinnerton-Dyer type'' by B. Mazur and J. Tate Commentary on algebra by B. Gross and J. Tate Some algebras associated to automorphisms of elliptic curves by M. Artin, J. Tate, and M. Van den Bergh The $p$-adic sigma function by B. Mazur and J. Tate Quantum deformations of $GL_n$ by M. Artin, W. Schelter, and J. Tate Modules over regular algebras of dimension 3 by M. Artin, J. Tate, and M. Van den Bergh Conjectures on algebraic cycles in $\ell$-adic cohomology by J. Tate The center of the 3-dimensional and 4-dimensional Sklyanin algebras by S. P. Smith and J. Tate The non-existence of certain Galois extensions of $\mathbb{Q}$ unramified outside 2 by J. Tate The centers of 3-dimensional Sklyanin algebras by M. Artin, W. Schelter, and J. Tate A review of non-Archimedean elliptic functions by J. Tate Homological properties of Sklyanin algebras by J. Tate and M. Van den Bergh Linear forms in $p$-adic roots of unity by J. Tate and J. F. Voloch Finite flat group schemes by J. Tate Bernard Dwork (1923-1998) by N. M. Katz and J. Tate Galois cohomology by J. Tate On a conjecture of Finotti by J. Tate Refining Gross's conjecture on the values of abelian $L$-functions by J. Tate On the Jacobians of plane cubics by M. Artin, F. Rodriguez-Villegas, and J. Tate Computation of $p$-adic heights and log convergence by B. Mazur, W. Stein, and J. Tate Letters by J. Tate

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Barry Mazur, Harvard University, Cambridge, MA, USA. Jean-Pierre Serre, College de France, Paris, France.

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