A Research Training Network of the European Union


 

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Work programme

Theme A. Arithmetic of varieties over local fields
Theme B. Arithmetic of varieties over global fields
Theme C. Automorphic forms and the Langlands programme


Numbers in square brackets [1,..] indicate the nodes participating in that part of the programme:

  [1]  Barcelona
  [2]  Bonn
  [3]  Cambridge
  [4]  Durham
  [5]  Jerusalem
  [6]  Milano
  [7]  Münster
  [8]  Padova
  [9]  Paris 11
[10]  Paris 13
[11]  Regensburg
[12]  Rennes
[13]  Strasbourg
[14]  Tokyo
 


 

Theme A : Arithmetic of varieties over local fields

  • A-1. Rigid Geometry [1, 2, 5, 7, 8, 9, 10, 11, 12, 13, 14]
     
    a) Foundations of rigid spaces and its derivates
    b) Generalization of p-adic analytic spaces and representability problems
     
  • A-2. Symmetric spaces [1, 2, 3, 5, 7, 10, 13]
     
  • A-3. Special varieties [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
     
    a) Curves and their fundamental groups
    b) Models of curves, jacobians and abelian varieties
    c) Abelian varieties, Shimura varieties and moduli problems
     
  • A-4. Singularities and bad reduction [4, 8, 9, 10, 12, 14].

    a) Ramification theory
    b) Logarithmic geometry and applications
     
  • A-5. Differential equations and de Rham cohomology [1, 5, 7, 8, 9, 10, 12, 14]
     
    a) Arithmetic properties of classical Picard-Fuchs equations
    b) Analytic methods and de Rham cohomology
    c) F-crystals and arithmetic theory of D-modules
     
  • A-6. p-adic cohomologies [1, 2, 5, 7, 8, 9, 10, 11, 12, 14]
     
    a) p-adic cohomologies of schemes in characteristic p
    b) p-adic cohomologies of schemes in mixed characteristic
    c) Comuutative group schemes, Dieudonné theory and generalizations
    d) Mixed p-adic Hodge structures
     
  • A-7. p-adic Galois representations [2, 3, 8, 9, 10, 11, 13, 14]
     
    a) Finite dimensional representations, de Rham and semi-stable representations
    b) (Phi, Gamma)-modules, Iwasawa theory and Galois modules
    c) Infinite dimensional Galois representations
     
  • A-8. Algorithmic problems [1, 6, 12]
     
     
  • Theme B : Arithmetic of varieties over global fields

  • B-1. L-functions and arithmetic [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14]
     
    a) p-adic L-functions and Iwasawa theory
    b) Motivic L-functions, Beilinson's and Bloch-Kato conjectures
    c) Non-vanishing results
     
  • B-2. Algebraic cycles and motives [1, 2, 3, 4, 5, 6, 9, 11, 13, 14]
     
    a) Chow groups and motivic cohomology
    b) Polylogarithms
    c) Higher class field theory
     
  • B-3. Arakelov theory [1, 2, 6, 7, 9, 11, 12]
     
  • B-4. Rational and integral points [3, 6, 8, 9, 12]
     
    a) Obstructions to the Hasse Principle
    b) Manin's conjectures on rational points
    c) Integral points
     
  • B-5. Shimura varieties and moduli spaces [1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14]
     
    a) Shimura varieties
    b) Elliptic curves and abelian varieties
    c) Function field variants and moduli spaces of bundles
     
  • B-6. Galois representations over global fields [4, 6, 9, 10, 12, 13, 14]
     
  • Theme C : Automorphic forms and the Langlands programme

  • C-1. Representations of reductive groups over local fields [5, 6, 7, 8, 9, 10, 12]
     
    a) Harmonic analysis on reductive groups over local fields
    b) Classification by types and Hecke algebras
    c) Local Langlands conjectures for classical groups
    d) Construction of discrete series L-packets
    e) Fundamental Lemmas
    f) Representation theory of reductive groups over local fields
    g) Modular representation theory of reductive groups over local fields
    h) p-adic representations of reductive groups over local fields
     
  • C-2. Trace formulas and functoriality [2, 4, 7, 9, 10, 13]
     
    a) Fundamental lemmas and stabilisation of the Arthur-Selberg trace formula
    b) Relative trace formulas and fine structure of L-packets
    c) Topological and geometric trace formulas
    d) Langlands conjectures over global fields
    e) Arthur conjectures on multiplicity of automorphic representations
     
  • C-3. Automorphic L-functions [1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14]
     
    a) L-functions of classical groups and converse theorems
    b) Construction of endoscopic representations and backwards lift to classical groups
    c) Special values of L-functions and related conjectures
    d) L-functions and construction of mixed motives
    e) Fine analytic properties of L-functions
     
     
  • C-4. p-adic theory of modular forms [1, 4, 5, 6, 7, 8, 9, 10, 11, 12]
     
    a) p-adic families of ordinary modular forms
    b) p-adic families of modular forms with positive slope
    c) Automorphic p-adic L-functions and Iwasawa theory
    d) Congruences of modular forms, arithmetic Hecke algebras, and deformations of Galois representations
    e) Modular forms mod p and generalisations of Serre's conjectures
     
  • C-5. Modular varieties and automorphic forms [1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13]
     
    a) Arithmetic of Shimura varieties over local and global fields
    b) Special points and André-Oort type conjectures
    c) Bad reduction of modular varieties and local models
    d) Arithmetic of modular and Shimura curves
    e) Drinfeld modular varieties and moduli of shtukas
    f) Cohomology of arithmetic groups and Eisenstein cohomology
     

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    © P. Berthelot
    Last update : 14.5.2004
     

    This network is a Marie Curie Research Training Network, supported by the European Commission under the Sixth Framework Programme (FP6)

    Contract : MRTN-CT2003-504917.