### Lectures on "Eigenvarieties for definite unitary groups"

##### Eigenvarieties semester, Harvard university, March-April 2006.

For some abstracts, see the relevant part of this
program (pages 3-4), and also Chung Pang Mok's newsletter.

The schedule.

Lecture 1 (*March
6*), * (phi,Gamma)-modules over the Robba ring*.
Lecture 2 (*March 13*), *The trianguline deformation functor of
a refined crystalline representation * (joint work with J. Bellaiche,
see chap. 2 of [2]).
Lecture 3 (*March 22*), *A p-adic interpolation of the
algebraic representations of the Iwahori subgroups* (see [1]).
Lecture 4 (*March 24*), *Eigenvarieties for definite unitary
groups* (see [1]).
Lecture 5 (*April 5*), *Residually multiplicity free
pseudocharacters * (joint work with J. Bellaiche, see chap. 1 of [2]).
Lecture 6 (*April 7*), *Trianguline properties of the family
of Galois representations on eigenvarieties * (joint work with J.
Bellaiche, see chap. 3, 4 of [2]).
Lecture 7 (*April 27*), *Eigenvarieties at non tempered
points and Selmer groups* (joint work with J. Bellaiche).

Some references for proofs of the statements given in the
talks (but see also the abstract above).

[1]. Chenevier G., *Familles p-adiques de formes automorphes pour
GL(n)*
Journal fur die reine und angewandte Mathematik 570, 143-217 (2004).

[2]. Bellaiche J., Chenevier G., *p-adic families of Galois representations
and higher rank Selmer groups.* ArXiv math.NT/0602340