Everything in these notes is essentially just rewriting the source material, up to occasional expansion on details, with no original material. Since everything is purely for my own benefit the writing may not be very clear.

• On Shimura varieties, following Milne:
  • Shimura data and varieties
  • Moduli interpretation
  • Complex multiplication
  • Canonical models
  • Counting points
• On local Shimura varieties, following Scholze-Weinstein:
  • Background: adic spaces, perfectoid spaces, and diamonds
  • Rapoport-Zink spaces
  • Moduli spaces of local shtukas
  • Integral models
• On modular forms and L-functions:
  • Tate's thesis
  • Overview of modular forms
  • The Rankin-Selberg method for modular forms
  • Geometric and arithmetic Siegel-Weil formulas