Student Algebraic Geometry
Organizer: Ben Church
Upcoming Events
"Some consequences of the Riemann hypothesis for varieties over finite fields" by Katz-Messing
[BO, section 8] + examples.
"Travaux de Dwork" by Katz
Past Events
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.
**Note room change for this date only due to qualifying exams being held in 384H**
Abstract
We will give an introduction to the classification of surfaces and 2d minimal model programme with a focus on low characteristic.
Introduction to the topic and proof that there is no elliptic curve over the integers using Weierstrass equations.
The refined patchworking theorem (Section 2.5.10–11 of [IMS09])