Seminar

Using a patching module without fixed level structure at primes dividing p (as in recent work of Caraiani, Emerton, Gee, Geraghty, Paskunas and Shin) one can construct some analogue of an eigenvariety. We show that this "patched eigenvariety" agrees (up to taking a product with some open polydisc) with a union of irreducible components of a space of trianguline representations. 

As a consequence we obtain some results about the local structure of eigenvarieties for unitary groups. This is joint work with C. Breuil and B. Schraen.