Algebraic Geometry for Number Theory (TCC)

Organiser: Florian Bouyer

Note: This is a study group and not a TCC lecture course. For a list of TCC course in Autumn click here

This study group will be trying to understand various topics in Algebraic Geometry and how they apply in a Number Theory context, with hopefully some concrete examples. All are welcomed and no pre-requisite in Algebraic Geometry are required (although having a general knowledge of varieties will help).

We aim to use a mixture of sources, including:

Algebraic Geometry: Robin Hartshorn
Algebraic Geometry and Arithmetic Curves: Qing Liu
Rational Points on Varieties: Bjorn Poonen

We will meet on Thursday between 9 and 11, from the 10th of October to 19th of December. The plan is to have a presentation for an hour and use the second hour as a discussion. What follows is a tentative outline of topics, this is very likely to change depending of the demands/suggestions made by people attending. Please contact me if you want to be on the mailing list organising the topics to cover.

Location: We meet in the TCC room. In Warwick this is room B0.06.

Other Resources: A list of resources that you might also find useful for further reading. Note that they vary in level of difficulty (from easy to "comprehensive").:

Goerge R. Kempf: Algebraic Varieties
Ravi's notes: http://math.stanford.edu/~vakil/216blog/ (Find the most recent version)
http://stacks.math.columbia.edu/

Schedule:

Date

Speaker

Topic

More Details

10th October

Florian Bouyer

Introduction and Sheaves.

Qing Liu pg 26-29,33-38. Some examples from Hartshorne
Notes I prepared for my talks: pdf. Slide for the week

17th October

Chris Williams

Schemes and Algebraic Varieties

Qing Liu pg 42-44. My typed up notes. Slides for the week

24th October

Pedro Lemos