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  1. virtualmath1.stanford.edu › ~rltaylorRichard Taylor's Home Page - Stanford University

    Richard Taylor rltaylor[@]stanford[dot]edu CV as of March 2023 (Former) Students : Dept. of Mathematics, Stanford University, Building 380, 450 Jane Stanford Way, Stanford, CA 94305-2125, U.S.A. tel. (650) 497-0640 Editor of: Journal of the AMS Forum of Mathematics Π and Σ : Some of this material is based upon work partially supported by the National Science Foundation

  2. virtualmath1.stanford.edu › ~rltaylor › cv6CURRICULUM VITAE NAME: Richard Lawrence Taylor - Stanford...

    NAME: Richard Lawrence Taylor DATE OF BIRTH: 19 May 1962 NATIONALITIES: US and British CAREER: 1980-84 BA, Cambridge University, England. 1984-88 PhD, Princeton University, U.S.A. (advisor Andrew Wiles). 1988-95 Fellow of Clare College, Cambridge. 1988-89 Royal Society European Exchange Fellow at Institut des Hautes Etudes Sci-enti ques, Paris.

  3. virtualmath1.stanford.edu › ~rltaylor › longicm02Galois Representations - Stanford University

    R. Taylor∗. Abstract. In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete sub-groups of Lie groups.

  4. virtualmath1.stanford.edu › ~rltaylor › cv23CURRICULUM VITAE DATE OF BIRTH: 19 May 1962 - Stanford University

    NAME: Richard Lawrence Taylor DATE OF BIRTH: 19 May 1962 NATIONALITIES: US and British CAREER: 1980-84 BA, Cambridge University, England. 1984-88 PhD, Princeton University, U.S.A. (advisor Andrew Wiles). 1988-95 Fellow of Clare College, Cambridge. 1988-89 Royal Society European Exchange Fellow at Institut des Hautes Etudes Sci-enti ques, Paris.

  5. virtualmath1.stanford.edu › ~rltaylor › irredAUTOMORPHY AND IRREDUCIBILITY OF SOME l-ADIC REPRESENTATIONS.

    AUTOMORPHY AND IRREDUCIBILITY OF SOME l-ADIC REPRESENTATIONS. STEFAN PATRIKIS AND RICHARD TAYLOR. Abstract. In this paper we prove that a pure, regular, totally odd, polar-izable weakly compatible system of l-adic representations is potentially auto-morphic.

  6. virtualmath1.stanford.edu › ~rltaylor › lg2LOCAL-GLOBAL COMPATIBILITY FOR l p, II. - Stanford University

    Abstract. We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associ-ated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GLn over an imaginary CM or totally real field.

  7. virtualmath1.stanford.edu › ~rltaylor › heckeRing Theoretic Prop erties of Certain Hec k e - Stanford...

    Theorem 1 The ring T is a c omplete interse ction. W e note that if O 0 is the ring of in tegers a nite extension K =K then the ring constructed using O 0 in place of is just T Q O . Also a complete in tersection if and only T O O 0 is (using for instance corollary 2.8 on page 209 of [K2]).

  8. virtualmath1.stanford.edu › ~rltaylor › shawReciprocity Laws and Density Theorems - Stanford University

    1 Introduction. This article is a written version of my 2007 Shaw Lecture. It is meant to explain the related ideas of reciprocity laws (such as quadratic reciprocity and the Shimura-Taniyama conjecture) and of density theorems (such as Dirichlet’s theorem and the Sato-Tate conjecture) to a general audience.

  9. virtualmath1.stanford.edu › ~rltaylor › cmpotautoPotential automorphy over CM fields - Stanford University

    Helm, Bao V. Le Hung, James Newton, Peter Scholze, Richard Taylor, and Jack A. Thorne Abstract Let F be a CM number eld. We prove modularity lifting theorems for regular n-dimensional Galois representations over F without any self-duality condition. We deduce that all elliptic curves E over F are potentially mod-

  10. virtualmath1.stanford.edu › ~rltaylor › cmpotauto2Abstract - Stanford University

    Helm,Bao V. LeHung, JamesNewton, Peter Scholze,Richard Taylor, and Jack A.Thorne Abstract Let F be a CM number field. We prove modularity lifting theorems for regular n-dimensional Galois representations over F without any self-duality condition. We deduce that all elliptic curves E over F are poten-