Towards Arithmetic Geometry
Since Autumn 2021, we are running w/ Alberto Cobos a course in Algebraic Geometry directed towards number theory PGRs, which will eventually lead us to the study of fundamental Arithmetic Geometry. The goal is, after reviewing concepts from basic algebraic geometry, to work towards the formulation of the Weil Conjectures, seeing Étale and Crystalline Cohomology in action, the understanding of the Mordell-Weil and Faltings theorems, reviewing Taniyama-Shimura modularity and the relation between Shimura Varieties and Holomorphic Automorphic Forms.
Main references (pour le moment):
Meetings take place Mondays at 13:00 in J11
Program:
Autumn 2021
Algebraic Geometry I ( 18.10.21)
Algebraic Geometry II (25.10.21)
Algebraic Geometry III ( 08.11.21)
Algebraic Geometry IV (Alberto Cobos- 15.11.21)
Algebraic Geometry V ( 29.11.21)
Algebraic Geometry VI (06.12.21)
Algebraic Geometry VII (13.12.21)
Algebraic Geometry VIII (Alberto Cobos- 20.12.21)
Spring 2022
The Picard Group and Algebraic Curves ( Alberto Cobos-03.22)
A Masterclass on The Geometry of Elliptic Curves (.03.22)
Lectures on Cohomology for the Arithmetically Inclined I (Menelaos- 03.22)
Lectures on Cohomology for the Arithmetically Inclined II (Menelaos- 03.22)
Elliptic Curves in Finite Characteristic
Elliptic Curves in Mixed Characteristic
Diophantine Approximation and a Theorem of Shafarevich on Integrality
Tate-Shafarevich and Mordell-Weil
