2005-06 Number Theory Learning Seminar

Organized by Brian Conrad and Chris Skinner

This year's topic is Serre's conjecture. Our goal is to get an understanding of the workings of Khare's proof in level 1, and more importantly of a sizable chunk of the serious background inputs that he uses in his proof (such as work of Taylor, Ramakrishna, and others, as well as more standard background in Galois cohomology, Galois representations, and arithmetic geometry). There are some excellent references, so most talks will not be written up. However, in some cases it may be decided to write up a few of the topics.

Outline for the year: pdf.
Serre's conjectures and modular curves: pdf.
Overview of Moret-Bailly's theorem on global points pdf.
Level-lowering and easy tameness criterion pdf.
Gauss-Manin connection and theta operator pdf.