Topics in Algebraic Geometry, Spring 2013

Teachers: Lenny Taelman, David Holmes.

Time: Mondays, 13:45--15:30. Place: Room 402, Snellius

Week 1: An introduction to schemes, and a discussion of arrangements for the remainder of the semester

Week 2.1: Johan Commelin; Projective and Noetherian schemes

Week 2.2: Milan Lopuhaä; Reduced and integral schemes

Week 3.1: Abtien Javanpeykar; Dimension

Week 3.2: Wouter Zomervrucht; base change

Week 4.1: Herman Hohrbach; Liu, 3.2.1 and 3.2.2 (algebraic varieties)

Week 4.2: Erik Massop; Liu, 3.2.3 (points taking values in field extensions)

Week 5.1: Erik Visse: separated and proper morphisms

Week 5.2: Tristan Tilly: a proof that projective implies proper

Week 6.1(11th March): Lenny Taelman: the functor of points

Week 6.2: Michele Serra: birational morphisms, normal varieties, ...

Week 7.1 (18th March): Niels uit de Bos: Zariski's Main Theorem

Week 7.2: Johan Commelin: Good reduction

Two week break for Easter

Week 8.1 (8th April): Chiara Damiolini: Braid groups and mapping class groups

Week 8.2: Jinbi Jin: Division polynomials for elliptic curves

Week 9.1 (15th April): David Holmes: Smooth morphisms

Week 9.2: Wouter Zomervrucht: sites

Week 10.1 (22nd April) Michele Serra: The Theorem of Deligne-Mumford

Week 10.2: Erik Visse: Finite flat group schemes

No seminar 29th April

Week 11.1 (6th May): Milan Louphaa: Shimura varieties

Week 11.2: David Holmes: Moduli of elliptic curves

Week 12.1 (13th May): Tristan Tilly: fundamental groups of schemes

Week 12.2: Abtien Javanpeykar : Cech cohomology

No seminar 20th May

Week 13.1 (27th May) [Probably no seminar]: TBA : TBA

Week 13.2: TBA : TBA

Algebra Seminar

Students attending this course may also be interested in attending the Algebra Seminar, which is held periodically on Mondays and Thursdays. Any students who are interested should email Ronald van Luijk to be added to his mailing list.

Participants:

Abtien Javanpeykar

Albert Gunawan

Chiara Damiolini

Erik Massop

Herman Rohrbach

Johan Commelin

Michele Serra

Niels uit de Bos

Wouter Zomervrucht

Milan Lopuhaä

Tristan Tilly

Course outline

All students writing their master theses in the Spring of 2013 in the area of algebra, geometry and number theory, or planning to start doing so in the near future, are advised to participate.

The rules for obtaining 6 EC for this seminar are as follows:

• speak at least two times;
• not too much of the same;
• there must be some originality in the talk (e.g., at least work out an example of yourself, or state and prove your own new theorem!);
• students provide notes for their own lectures.

To get an idea of possible topics, see the program of 2011. This year's program (only Spring 2013) will be built up as time goes by.