Tate has assembled his 78 published mathematical papers and 20 of his letter, mostly to J-P. Serre, his principle correspondent. The arrangement is chronological, in the first volume, the papers then the letters 1951-75, and in the second volume 1976-2006. Among the topics are genus change in inseparable extensions of functional fields, the homology of noetherian rings and local rings, the cohomology groups of tori in infinite Galois extensions of number fields, an algorithm for determining the type of a singular fiber in an elliptic pencil, variation of the canonical height of a point depending on a parameter, the non-existence of certain Galois extensions of Q unramified outside two, and refining Gross' conjecture on the values of abelian L-functions. Annotation ©2017 Ringgold, Inc., Portland, OR (protoview.com)
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
Barry Mazur, Harvard University, Cambridge, MA, USA.
Jean-Pierre Serre, College de France, Paris, France.
