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

About the Author

Barry Mazur, Harvard University, Cambridge, MA, USA.

Jean-Pierre Serre, College de France, Paris, France.