Arithmetic and Algebraic Geometry Seminar

Korteweg-de Vries Instituut, University of Amsterdam

This is the website for the Arithmetic and Algebraic Geometry seminar at the University of Amsterdam.

This semester the lectures alternate between a study group on crystalline cohomology and research talks that are not necessarily related to the study group. The first goal of the study group is to understand crystalline cohomology, its motivation, definition, properties and the main examples. Once this is done we will decide on some further interesting topics to cover (there are of course many!).

Topics:

• Classical Dieudonne Theory
• Infinitesimal cohomology over C (this will give motivation for the crystalline theory later)
• Background on sites and cohomology
  • The infinitesimal site, crystals, connections
  • de Rham cohomology
  • Relations between H_inf, H_dR and H_Betti. Also, universal vector extensions.
• Crystalline cohomology
  • Why crystalline cohomology?
  • Divided powers, the crystalline site
  • Crystalline cohomology and its properties (Frobenius, filtrations, connection)
  • Comparison between H_crys and H_dR of a smooth lift.
  • H^1_crys of abelian varieties and the Dieudonne module of its p-divisible group (universal vector extensions)
• Applications/Further topics to be decided.

0x50 0x72 0x65 0x72 0x65 0x71 0x75 0x69 0x73 0x69 0x74 0x65 0x73: Some algebraic geometry, category theory and homological algebra.

Practical Information

Calendar