Galois representations (2010, L24)

This is a website for the Part III (Graduate Level; non-examinable) course Galois Representations (2010, L24); here are some material for this course.

------ time

Meetings: Tue / Thu / Sat 10am, at MR 11.
First lecture: Thu., 14th January, 2010.

------ syllabus (from the official website of the department)

  • p.28 of the [pdf] Guide to Courses (Part III).

    ------ notes

  • [pdf] Notes (last update 29/1/10)

    Rough record of what we've covered:

  • Lecture 1 (Th. 14/1/10): Intro I (Intro)
  • Lecture 2 (Sa. 16/1/10): Intro II (Galois representations)
  • Lecture 3 (Tu. 19/1/10): Intro III (Automorphic representations)
  • Lecture 4 (Th. 21/1/10): Intro IV (Motives)
  • Lecture 5 (Sa. 23/1/10): Class field theory of Q (classical)
  • Lecture 6 (Tu. 26/1/10): Class field theory of Q (via adeles)
  • Lecture 7 (Th. 28/1/10): Local class field theory and local/global compatibility for Q
  • Lecture 8 (Sa. 30/1/10): Global class field theory for number fields and l-adic characters of Q
  • Lecture 9 (Tu. 2/2/10): GCFT of algebraic Hecke/Galois characters of Q
  • Lecture 10 (Th. 4/2/10): GCFT of algebraic Hecke/Galois characters of number fields
  • Lecture 11 (Sa. 6/2/10): Q&A, l-adic charaters are unramified at a.a.primes
  • Lecture 12 (Tu. 9/2/10): Theorems on algebraic Hecke/Galois characters

    ------ literature

    Here are some references mentioned in the lectures. Just for the sake of records - they are not essential at all.

  • Local class field theory:
    [pdf] T. Yoshida, Local class field theory via Lubin-Tate theory, Annales de la Faculte des Sciences de Toulouse, Ser. 6, 17-2 (2008), 411-438.
  • Profinite groups:
    [amazon] J. Neukirch, A. Schmidt, K. Wingberg, Cohomology of Number Fields, Grundlehren der Mathematischen Wissenschaften 323, Springer, 2000.
  • Lefschetz fixed point formula:
    [amazon] R. Bott, L. W. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Mathematics 82, Springer, 1982.
  • Motives, Cohomology:
    [ams] U. Jannsen, S. Kleiman, J.-P. Serre, ed., Motives, Proc. Symp. Pure Math. 55, AMS, 1994.
  • Fontaine-Mazur conjecture:
    [scan] J.-M. Fontaine, B. Mazur, Geometric Galois Representations, in: Elliptic Curves, Modular Forms and Fermat's Last Theorem (J. Coates and S.-T. Yau, eds., International Press, 1995), 41-78.

    maintained by Teruyoshi Yoshida
    Last modified: Feb. 9, 2010.