F_p-représentations semi-stables

Abstract

37 pagesInternational audienceTorsion semi-stable representations can be constructed and studied using Breuil modules. In this paper, we define the notion of pylonet and prove that some categories of Breuil modules naturally define pylonets. As a consequence, we are able to define full subcategories of Breuil's categories with very nice properties (in particular, they are abelian). In a second part of this work, we try to make very explicit some abstract constructions coming from the general theory of pylonets (developped earlier in the paper). These explicitations should be very useful to make computations with torsion semi-stable Galois representations

On the weights of mod p Hilbert modular forms

“…Of course, we wish to know the corresponding objects of BrMod p−2 dd . This is straightforward: by Proposition 4.2.2 of [Car09], and the discussion preceding and following it, we see that we can obtain the requisite modules by simply taking the extension of scalars k[u]/u p → k[u]/u ep given by u → u e , and allowing Gal(K/K 0 ) to act via its action on k[u]/u ep . We obtain the following general form:…”

On mod p local-global compatibility for GL3(Qp) in the non-ordinary case

“…We remark that this definition is compatible with the notion of duality on Breuil and strongly divisible modules as defined in , namely and .…”

“…The functor respects the rank on both sides, that is, (cf. [, Theorem 4.2.4] and the Remark following it, see also [, Lemma 3.2.2])…”

Serre weights for three-dimensional ordinary Galois representations

“…None of the results in this section is new: they build on classical work of Breuil and Caruso (cf. for instance [4,10]) and we refer the reader to [28, Section 2] for a concise reference. We keep the notations and conventions of Section 1.…”