Collected Works of John 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. TatePart II: Problem 9: The general reciprocity law by J. TateRelations between $K_2$ and Galois cohomology by J. TateLocal constants by J. T. TateOn the torsion in $K_2$ of fields by J. TateFields medals (IV): An instinct for the key idea by J. TateA simple proof of the main theorem of elimination theory in algebraic geometry by P. Cartier and J. TateNumber theoretic background by J. TateThe Harish-Satake transform on $GL_r$ by J. TateBrumer-Stark-Stickelberger by J. TateOn conjugation of abelian varieties of CM type by J. TateOn Stark's conjectures on the behavior of $L(s,\chi)$ at $s=0$ by J. TateVariation of the canonical height of a point depending on a parameter by J. TateA reciprocity law for $K_2$-traces by S. Rosset and J. TateCanonical height pairings via Biextensions by B. Mazur and J. TateOn $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer by B. Mazur, J. Tate, and J. TeitelbaumRefined conjectures of the ``Birch and Swinnerton-Dyer type'' by B. Mazur and J. TateCommentary on algebra by B. Gross and J. TateSome algebras associated to automorphisms of elliptic curves by M. Artin, J. Tate, and M. Van den BerghThe $p$-adic sigma function by B. Mazur and J. TateQuantum deformations of $GL_n$ by M. Artin, W. Schelter, and J. TateModules over regular algebras of dimension 3 by M. Artin, J. Tate, and M. Van den BerghConjectures on algebraic cycles in $\ell$-adic cohomology by J. TateThe center of the 3-dimensional and 4-dimensional Sklyanin algebras by S. P. Smith and J. TateThe non-existence of certain Galois extensions of $\mathbb{Q}$ unramified outside 2 by J. TateThe centers of 3-dimensional Sklyanin algebras by M. Artin, W. Schelter, and J. TateA review of non-Archimedean elliptic functions by J. TateHomological properties of Sklyanin algebras by J. Tate and M. Van den BerghLinear forms in $p$-adic roots of unity by J. Tate and J. F. VolochFinite flat group schemes by J. TateBernard Dwork (1923-1998) by N. M. Katz and J. TateGalois cohomology by J. TateOn a conjecture of Finotti by J. TateRefining Gross's conjecture on the values of abelian $L$-functions by J. TateOn the Jacobians of plane cubics by M. Artin, F. Rodriguez-Villegas, and J. TateComputation of $p$-adic heights and log convergence by B. Mazur, W. Stein, and J. TateLetters by J. Tate