North of England Algebraic Number Theory Group

Seventh meeting, Durham (4/5/2002)

The seventh meeting was on Saturday May 4th in Durham. The programme was as follows:

• 11.00-12.00 Helena Verrill (Hannover)

  Modular symbols for Γ₀(N) in weight k>2

  Abstract: I will talk about some of the differences between the weight 2 case and higher weight case, such as "transportable symbols" which William Stein and I define in a recent paper.

• 12.00-13.30 LUNCH BREAK
• 13.30-14.30 Mikhail Bondarko (St.Petersburg)

  Cohomology of formal group moduli

  Abstract: A connection is established between the additive Galois module structure of ideals in an extension of complete discrete valuation field and cohomology of formal group modules. Using that, Galois module structure of a wide class of totally ramified extensions is described completely.

• 14.30-14.45 break
• 14.45-15.45 Jayanta Manoharmayum (Sheffield)

  Serre's Conjecture: the case of GL₂(F₇)

  Abstract: There is now a general procedure for proving Serre's conjecture - simply find points defined over a soluble extension on an appropriate moduli space and use base change results. This process can be implemented in the case of Galois representations with values in GL₂(F₇) under some local conditions. I shall explain the proof (for the case of GL₂(F₇) and talk about the general process.

• 15.45-16.00 coffee
• 16.00-17.00 Tim Dokchitser (Durham)

  Local deformation problems for abelian varieties

  Abstract: We discuss various approaches to study local deformation problems related to abelian varieties (known as PEL-type problems) and describe the solution in "rigid" cases.

Frazer Jarvis, May 5th, 2002.