Topics in Arithmetic Geometry, Fall 2013
« Fourier Transform in Algebraic Geometry »

Course Information

• Syllabus
• Ceiba
• Lectures: Tuesday and Friday, 9:00 - 10:30 AM at Astro-Math 102 and 101, respectively
• References:
  • Deligne, SGA 4½.
  • Deligne, La conjecture de Weil. II (1980).
  • Henniart, Les inéqualités de Morse (d'après E.Witten), Bourbaki nº 617.
  • Katz, Local-to-global extensions of representations of fundamental groups (1986).
  • Katz, Travaux de Laumon, Bourbaki nº 691.
  • Katz, L-functions and monodromy: four lectures on Weil II (2001).
  • Laumon, Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil (1987).
  • Witten, Supersymmetry and Morse theory (1982).

Contents

1. Witten's stationary phase principle in Riemannian geometry
2. Laumon's stationary phase principle
1. Fundamental groups and lisse sheaves
2. Gabber-Katz extension
3. Derived category of constructible l-adic sheaves
4. Fourier transform; examples
5. Local Fourier
6. Applications
7. Explicit formulas
3. The principle for connections

Supplementary

• The plan for a nonexistent summer seminar about étale fundamental groups
• The LaTeX-file and the pdf-file for the solutions (written by students) to some exercises in Lenstra's Galois theory for schemes

Last updated on 2014.1.9.