Student Algebraic Geometry

Abstract

"Travaux de Dwork" by Katz

[BO, section 8] + examples.

"Some consequences of the Riemann hypothesis for varieties over finite fields" by Katz-Messing

Katz-Oda + [BO, section 7]. 

[BO, 7.1-7.11] and Theorem 1.3 of F-isocrystals and de Rham cohomology. I (Berthelot-Ogus, Inventiones).

HPD-stratifications [BO, 4.1-4.4], and crystals [BO, 6.1-6.6]

definition of crystalline cohomology, functoriality [BO, 5.4-19], and connections [BO, 2.1-2.10].

The need for divided powers + grothendieck's philosophy [BO, 1.11], PD-structures, PD-thickening, the cystalline site [BO, 3.1-5, 3.12-17, 5.1-3]

I will review the Picard-Fuchs equation for the Legendre family fixing erros from last time and review the theory of the Gauss-Manin connection.

This lecture will be independent of the following weeks.