Cohen Lenstra over Function Fields
This is the webpage for the reading seminar at the University of California Irvine. The main goal is to understand the main tools in the paper http://annals.math.princeton.edu/2016/183-3/p01.
This will be regularly updated with materials, comments on the lectures and speaker.
We currently intend to cover the following list of topics :
- Overview of the paper: Goals for the reading seminar
- Jiayi Shen - 18th of October "Number fields"
- Fei Xiang- 25th of October "Algebraic geometry in function fields"
- Number field and function field analogies
- Weil conjectures
- Singular cohomology
- Etale Cohomology; Kummer Theory
- Homological Representation Stability
This was the end of the first quarter. Here are some useful links to materials for the above lectures:
This was the end of the first quarter. Here are some useful links to materials for the above lectures:
- Some survey notes on Number Fields notions we need http://www.jchl.co.uk/maths/Number.pdf
- Some algebraic geometry notions we need http://math.mit.edu/classes/18.782/LectureNotes19.pdf
- Renne Schoof Notes on Arakelov Class Group http://websites.math.leidenuniv.nl/algebra/Schoof-Arakelov.pdf
- Analogies between function fields and number fields by Jordan Ellenberg http://swc.math.arizona.edu/aws/2014/2014EllenbergNotes.pdf
- Kowalski's notes on the Weil Conjectures: https://people.math.ethz.ch/~kowalski/deligne.pdf
- Popa's notes on points over finite fields https://sites.math.northwestern.edu/~mpopa/571/chapter2.pdf
- Kummer Theory https://ayoucis.wordpress.com/2015/08/17/kummer-theory-and-the-weak-mordell-weil-theorem/
- Tom Lovering's notes on Etale cohomology https://tlovering.files.wordpress.com/2012/06/essay-body1.pdf
- Singular Cohomology http://www-personal.umich.edu/~mmustata/appendix_cohomology.pdf
- Homological Representation Stability by Benson Farb https://people.maths.ox.ac.uk/tillmann/FarbICM.pdf
- Homological Representation Stability Jenny Wilson http://www.math.lsa.umich.edu/~jchw/OberwolfachTalk-IntroductionToRepStability.pdf
We will continue the seminar this winter quarter. Here are the topics leftover:
We will continue the seminar this winter quarter. Here are the topics leftover:
- Arithmetic Statistics
- Moduli Spaces and Classifying Spaces
- Hurwitz Schemes