Topics in Arithmetic Geometry, Spring 2011

Time: Mondays, 15:45--17:30. Place: Snellius 401.

All students writing their master theses in the Spring of 2010 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 last year's program. This year's program (only Spring 2011) will be built up as time goes by.

May 16

• 16:45, Michiel Kosters, Groups acting on rings - a theorem of Tate.
• 15:45, Davide Calliari, Group law on the smooth part of a singular cubic curve.

May 9

• 16:45, Maarten Derickx, Order and specialisation of torsion points.
• 15:45, Albert Gunawan, Complete local rings and quotients of varieties by actions of finite groups.

April 25 and May 2

• No lectures (2nd day of easter, and absence of Bas and Peter).

April 18

• 16:45, Ariyan Javanpeykar, continued.
• 15:45, Ariyan Javanpeykar, Heights.

April 11

• 15:45. Julio Brau, Galois representations attached to elliptic curves without complex multiplication.

April 4

• 16:45. Bas Edixhoven: continuation.
• 15:45. Bas Edixhoven, Daniel Bertrand's counter example to the relative Manin-Mumford conjecture for semi-abelian varieties.

March 28

• No lectures.

March 21

• 16:45. Albert Gunawan, Two properties of rings of invariants for finite group actions on rings.
• 15:45. Nils Bruin, On primes p with class number of Q(\sqrt{-4p}) divisible by 16.

March 14

• Sunil Rana, Manifolds and Locally ringed spaces.
• Athanasios Angelakis, Ulm's theorem.

March 7

• Davide Calliari, Construction of cubic surfaces from 6 points in the projective plane.
• Michiel Kosters, The geometry of a finite group acting on a ring. He will prove Proposition 9.1.1 in here. Here are his notes

February 28

• Ariyan Javanpeykar, Locally ringed spaces, affine schemes.

February 21

• No course because Peter and Bas are in Padova.

February 14

• Maarten Derickx, Symmetric products of varieties.
• Jinbi Jin, Construction of some modular curves, part 2.

February 7

• Maarten Derickx, Quotients by finite groups acting on varieties.
• Jinbi Jin, Construction of some modular curves.

January 31. First meeting.

• Organisational part.
• Bas Edixhoven, introduction to torsion points on elliptic curves over number fields. Here are my notes of a lecture by Michael Stoll.