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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:

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
More on Schemes
Hartshorne. My typed up notes. Slides for the week
31st October

Chris Birkbeck

Basic Properties of Schemes (e.g. Integral, Neotherian, etc)
7th November
 Adam Morgan
Sheaves of Modules (Part 1)

Hartshorne, Chapter II sect. 5.
My typed up notes. Slides for the week

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
5th December
 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