Adèles, idèles and Tate's thesis

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Restricted products, adèles and idèles of number fields, ray class groups, additive Fourier analysis and Poisson summation, Tate zeta integrals and Hecke L-functions, and the local tree and spherical Hecke algebra of GL₂.

  1. Restricted products and profinite completions
  2. The adèle ring of a number field
  3. Idèles and the idèle class group
  4. Idèles, ideals and ray class groups
  5. Additive characters, self-dual measures and Poisson summation on the adèles
  6. Quasi-characters and Hecke characters
  7. Tate's local theory at the finite places
  8. Tate's local theory at the infinite places
  9. Tate's global theory: continuation and functional equation
  10. Hecke L-functions and the Dedekind zeta function
  11. Lattices over a local field: the tree of GL₂ and its decompositions
  12. The spherical Hecke algebra of GL₂ and Hecke operators on lattices

Original course text: CC0. The marked edge-stabilizer adaptation in lesson 11: CC BY 4.0. Source credits and changes appear in the lessons. MathJax and font licences are retained in the assets folder.