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)
|Introduction and Sheaves.
|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
||More on Schemes
||Hartshorne. My typed up notes. Slides for the week
|31st October||Basic Properties of Schemes||(e.g. Integral, Neotherian, etc)|
|| Adam Morgan
||Sheaves of Modules (Part 1)
|14th November||Adam Morgan||Sheaves of Modules (Part 2)||Hartshorne, Chapter II sect. 5
My typed up notes. Slides for the week
|21st November|| Celine Maistret
||Divisors||Hartshorne, Silverman. My typed up notes. Slides for the week
|28th November||Ian Vincent||Morphisms and Blowing Up||My typed up notes. Slides for the week
||Samuele Anni||Minimal Models and Integral Models
||My typed up notes. Slides for the week.
Note that algorithm to find minimal models have been
implemented this september, for genus less than and equal to 2.
|12th December|| Jeroen Sijsling
||More minimal models
||My typed up notes. Slides for the week|
|19th December||Jeroen Sijsling||More minimal models||My typed up notes. Slides for the week|