Breuil-le-Sec

Breuil Modules for Raynaud Schemes

Let p be an odd prime, and let OK be the ring of integers in a finite extension K/Qp. Breuil has classified finite flat group schemes of type (p, . . . , p) over OK in terms of linear-algebraic objects that have come to be known as Breuil modules. This classification can be extended to the case of finite flat vector space schemes G over OK . When G has rank one, the generic fiber of G correspon...

The Breuil–mézard Conjecture for Quaternion Algebras

We formulate a version of the Breuil–Mézard conjecture for quaternion algebras, and show that it follows from the Breuil–Mézard conjecture for GL2. In the course of the proof we establish a mod p analogue of the Jacquet– Langlands correspondence for representations of GL2(k), k a finite field of characteristic p.

Locally algebraic vectors in the Breuil – Herzig ordinary part

For a fairly general reductive group G/Qp , we explicitly compute the space of locally algebraic vectors in the Breuil–Herzig construction (ρ)ord , for a potentially semistableBorel-valued representationρ ofGal(Q̄p/Qp). The point beingwedealwith thewhole representation, not just its socle—and we go beyond GLn(Qp). In the case of GL2(Qp), this relation is one of the key properties of the p-adic l...

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