ICTP Mathematics Seminar - Wednesday 16 December, at 14:00

[Math Group]

M A T H E M A T I C S   S E M I N A R S   2015


Wednesday 16 December, at 14:00 hrs.


Lassina Dembele (University of Warwick)


Title: Serre weights and wild ramification in two-dimensional Galois 
representations


Abstract: Let $F$ be a totally real number field, $p\ge 2$ a rational
prime, and $\overline{\rho}: {\rm Gal}(\overline{F}/F) \to {\rm
GL}_2(\overline{{\bf F}}_p)$ a Galois representation arising from a
Hilbert modular form. The weight part of Serre's Conjecture
(proved by Gee et al) determines the set of weights
$\mathcal{D}(\overline{\rho})$ of forms from which $\overline{\rho}$
arises. However the dependence of the set $\mathcal{D}(\overline{\rho})$
on wild ramification is not explicit. I'll discuss joint work with
Diamond and Roberts towards making it so. This amounts to describing
wild ramification in reductions of two-dimensional crystalline Galois
representations.


Venue:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)


-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building, room 106
Strada Costiera no. 11
34151 Trieste, Italy

Tel. no.: +39-040-2240455
math at ictp.it
http://math.ictp.it