We construct explicitly some analytic families of étale (φ, Γ)-modules, which give rise to
analytic families of 2-dimensional crystalline representations. As an application of our …

In this paper we give criteria for the modularity of certain two-dimensional Galois
representations. Originally conjectural criteria were formulated for compatible systems of X …

Let p be an odd prime, ka finite field of characteristic p, and W (k) the ring of Witt vectors of k.
The study of Galois representations p: GQ Gal (Q/Q)-+ GL2 (k) and their deformations to …

Nous conjecturons que la réduction modulo des représentations cristallines irréductibles de
dimension 2 sur peut être prédite par la réduction modulo. Nous explicitons quelques …

We examine the deformation theory of two dimensional mod $ p $ reducible
indecomposable Galois representations, removing or relaxing many of the hypotheses of …

Let p> 2 be prime. We use purely local methods to determine the possible reductions of
certain two-dimensional crystalline representations, which we call pseudo-Barsotti–Tate …

Let S be a base scheme in characteristic p. Consider the crystalline Dieudonne module
functor D on the category of^-divisible groups over S to the category of Dieudonne crystals …

In this paper we establish the modularity of certain p-adic representations of Gal (F/F), where
F is a totally real field. The main conditions imposed are that p be odd, the representation be …

Once we know the crystal associated with representations, we can read for example the
branching rule, decomposition into irreducible components of tensor products, etc. Hence it …

In this paper we study Siegel modular forms of degree three. We give (i) 34 generators of the
graded ring A (F3) of modular forms, and (ii) the generating functions of A (F3). A dimension …