Stefano Marseglia


at Rennes University

Mini-course: Ideal classes and abelian varieties over finite fields.

Info:
The course will take place on 12-13-14-15 November 2018.
Each lecture will be 2h long.
Overview:
This mini-course will be divided in two parts. In the first we will discuss how to compute all ideal classes of a non-maximal order in étale Q-algebras (i.e. products of number fields). In the second part we will introduce abelian varieties over finite fields and we will describe them by mean of a much more concrete category, which, under certain assumptions, can be described in terms of fractional ideals.
Lectures:
1) Introduction - √Čtale Q-algebras, orders, fractional ideals (invertible and non).
2) Ideal classes, Picard Groups and Ideal Class Monoids.
3) Abelian varieties over finite fields - basic definitions, Honda-Tate theory.
4) Categorical descriptions - Theorems of Deligne and Centeleghe-Stix and computations using ideal classes.
Material:
- Lecture 1 - Lecture 2 - Lecture 3 - Lecture 4
- Magma Examples
- In the 4th lecture and in the magma examples there is also material regarding the connection between conjugacy classes of integral matrices and ideal class monoid, which I did not have time to cover in class.

at Stockholm University

How dows it work?
In Sweden the PhD studies are usually 4 years long. If the PhD student decides to teach he/she will obtain an extension of 1 year. In this case the work load will be divided in 80% for research and 20% teaching. This consists of 300 hours of teaching duties per academic year, which can be divided flexibly according to the students needs. The teaching for Bachelor courses is in Swedish, while it is in English for the Master Level.

Spring 2018:
- Lectures and Examination, Mathematics of cryptography, English
Spring 2017:
- Exercise sessions and Grading, Mathematics of cryptography, English
- Tutoring (Handledning), Matematik I, Swedish
Fall 2016:
- Exercise sessions and Grading, Commutative Algebra and Algebraic Geometry, English
- Grading - Abstract Algebra, English
- Tutoring (Handledning), Matematik I, Swedish
Spring 2016:
- Exercise sessions and Grading, Mathematics of cryptography, English
- Tutoring (Handledning), Matematik I, Swedish
- Tutoring (Handledning), Lilla Bibliotek, Swedish
Fall 2015:
- Tutoring (Handledning), Matematik I, Swedish
- Tutoring (Handledning), Lilla Bibliotek, Swedish
Spring 2015:
- Exercise sessions and Grading, Mathematics of cryptography, English
- Tutoring (Handledning), Matematik I, Swedish
- Tutoring (Handledning), Lilla Bibliotek, Swedish
Fall 2014:
- Tutoring (Handledning), Matematik I, Swedish
- Tutoring (Handledning), Lilla Bibliotek, Swedish
Spring 2014:
- Exercise sessions and Grading, Mathematics of cryptography, English