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

• Part I: Fourier analysis in number fields and Hecke's zeta-functions by J. T. TateA note on finite ring extensions by E. Artin and J. T. TateOn the relation between extremal points of convex sets and homomorphisms of algebras by J. TateGenus change in inseparable extensions of function fields by J. TateOn Chevalley's proof of Luroth's theorem by S. Lang and J. TateThe higher dimensional cohomology groups of class field theory by J. TateThe cohomology groups of algebraic number fields by J. T. TateOn the Galois cohomology of unramified extensions of function fields in one variable by Y. Kawada and J. TateOn the characters of finite groups by R. Brauer and J. TateHomology of Noetherian rings and local rings by J. TateWC-groups over $p$-adic fields by J. TateOn the inequality of Castelnuovo-Severi by E. Artin and J. TateOn the inequality of Castelnuovo-Severi, and Hodge's theorem by J. TatePrincipal homogeneous spaces over abelian varieties by S. Lang and J. TatePrincipal homogeneous spaces for abelian varieties by J. TateA different with an odd class by A. Frohlich, J.-P. Serre, and J. TateNilpotent quotient groups by J. TateDuality theorems in Galois cohomology over number fields by J. TateRamification groups of local fields by S. Sen and J. TateFormal complex multiplication in local fields by J. Lubin and J. TateAlgebraic cycles and poles of zeta functions by J. T. TateElliptic curves and formal groups by J. Lubin, J. Serre, and J. TateOn the conjectures of Birch and Swinnerton-Dyer and a geometric analog by J. TateFormal moduli for one-parameter formal Lie groups by J. Lubin and J. TateThe cohomology groups of tori in finite Galois extensions of number fields by J. TateGlobal class field theory by J. T. TateEndomorphisms of abelian varieties over finite fields by J. TateThe rank of elliptic curves by J. T. Tate and I. R. SafarevicResidues of differentials on curves by J. Tate$p$-divisible groups by J. T. TateThe work of David Mumford by J. TateClasses d'isogenie des varietes abeliennes sur un corps fini (d'apres T. Honda) by J. TateGood reduction of abelian varieties by J.-P. Serre and J. TateGroup schemes of prime order by J. Tate and F. OortSymbols in arithmetic by J. TateRigid analytic spaces by J. TateThe Milnor ring of a global field by H. Bass and J. TateAppendix by H. Bass and J. TateLetter from Tate to Iwasawa on a relation between $K_2$ and Galois cohomology by J. TatePoints of order 13 on elliptic curves by B. Mazur and J. TateThe arithmetic of elliptic curves by J. T. TateThe 1974 Fields Medals (I): An algebraic geometer by J. TateAlgorithm for determining the type of a singular fiber in an elliptic pencil by J. TateLetters by J. Tate

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

• Part I: Fourier analysis in number fields and Hecke's zeta-functions by J. T. TateA note on finite ring extensions by E. Artin and J. T. TateOn the relation between extremal points of convex sets and homomorphisms of algebras by J. TateGenus change in inseparable extensions of function fields by J. TateOn Chevalley's proof of Luroth's theorem by S. Lang and J. TateThe higher dimensional cohomology groups of class field theory by J. TateThe cohomology groups of algebraic number fields by J. T. TateOn the Galois cohomology of unramified extensions of function fields in one variable by Y. Kawada and J. TateOn the characters of finite groups by R. Brauer and J. TateHomology of Noetherian rings and local rings by J. TateWC-groups over $p$-adic fields by J. TateOn the inequality of Castelnuovo-Severi by E. Artin and J. TateOn the inequality of Castelnuovo-Severi, and Hodge's theorem by J. TatePrincipal homogeneous spaces over abelian varieties by S. Lang and J. TatePrincipal homogeneous spaces for abelian varieties by J. TateA different with an odd class by A. Frohlich, J.-P. Serre, and J. TateNilpotent quotient groups by J. TateDuality theorems in Galois cohomology over number fields by J. TateRamification groups of local fields by S. Sen and J. TateFormal complex multiplication in local fields by J. Lubin and J. TateAlgebraic cycles and poles of zeta functions by J. T. TateElliptic curves and formal groups by J. Lubin, J. Serre, and J. TateOn the conjectures of Birch and Swinnerton-Dyer and a geometric analog by J. TateFormal moduli for one-parameter formal Lie groups by J. Lubin and J. TateThe cohomology groups of tori in finite Galois extensions of number fields by J. TateGlobal class field theory by J. T. TateEndomorphisms of abelian varieties over finite fields by J. TateThe rank of elliptic curves by J. T. Tate and I. R. SafarevicResidues of differentials on curves by J. Tate$p$-divisible groups by J. T. TateThe work of David Mumford by J. TateClasses d'isogenie des varietes abeliennes sur un corps fini (d'apres T. Honda) by J. TateGood reduction of abelian varieties by J.-P. Serre and J. TateGroup schemes of prime order by J. Tate and F. OortSymbols in arithmetic by J. TateRigid analytic spaces by J. TateThe Milnor ring of a global field by H. Bass and J. TateAppendix by H. Bass and J. TateLetter from Tate to Iwasawa on a relation between $K_2$ and Galois cohomology by J. TatePoints of order 13 on elliptic curves by B. Mazur and J. TateThe arithmetic of elliptic curves by J. T. TateThe 1974 Fields Medals (I): An algebraic geometer by J. TateAlgorithm for determining the type of a singular fiber in an elliptic pencil by J. TateLetters by J. Tate

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

• Part I: Fourier analysis in number fields and Hecke's zeta-functions by J. T. TateA note on finite ring extensions by E. Artin and J. T. TateOn the relation between extremal points of convex sets and homomorphisms of algebras by J. TateGenus change in inseparable extensions of function fields by J. TateOn Chevalley's proof of Luroth's theorem by S. Lang and J. TateThe higher dimensional cohomology groups of class field theory by J. TateThe cohomology groups of algebraic number fields by J. T. TateOn the Galois cohomology of unramified extensions of function fields in one variable by Y. Kawada and J. TateOn the characters of finite groups by R. Brauer and J. TateHomology of Noetherian rings and local rings by J. TateWC-groups over $p$-adic fields by J. TateOn the inequality of Castelnuovo-Severi by E. Artin and J. TateOn the inequality of Castelnuovo-Severi, and Hodge's theorem by J. TatePrincipal homogeneous spaces over abelian varieties by S. Lang and J. TatePrincipal homogeneous spaces for abelian varieties by J. TateA different with an odd class by A. Frohlich, J.-P. Serre, and J. TateNilpotent quotient groups by J. TateDuality theorems in Galois cohomology over number fields by J. TateRamification groups of local fields by S. Sen and J. TateFormal complex multiplication in local fields by J. Lubin and J. TateAlgebraic cycles and poles of zeta functions by J. T. TateElliptic curves and formal groups by J. Lubin, J. Serre, and J. TateOn the conjectures of Birch and Swinnerton-Dyer and a geometric analog by J. TateFormal moduli for one-parameter formal Lie groups by J. Lubin and J. TateThe cohomology groups of tori in finite Galois extensions of number fields by J. TateGlobal class field theory by J. T. TateEndomorphisms of abelian varieties over finite fields by J. TateThe rank of elliptic curves by J. T. Tate and I. R. SafarevicResidues of differentials on curves by J. Tate$p$-divisible groups by J. T. TateThe work of David Mumford by J. TateClasses d'isogenie des varietes abeliennes sur un corps fini (d'apres T. Honda) by J. TateGood reduction of abelian varieties by J.-P. Serre and J. TateGroup schemes of prime order by J. Tate and F. OortSymbols in arithmetic by J. TateRigid analytic spaces by J. TateThe Milnor ring of a global field by H. Bass and J. TateAppendix by H. Bass and J. TateLetter from Tate to Iwasawa on a relation between $K_2$ and Galois cohomology by J. TatePoints of order 13 on elliptic curves by B. Mazur and J. TateThe arithmetic of elliptic curves by J. T. TateThe 1974 Fields Medals (I): An algebraic geometer by J. TateAlgorithm for determining the type of a singular fiber in an elliptic pencil by J. TateLetters by J. Tate