Related papers: Filtered modules corresponding to potentially semi…

Suppose $\rho_1, \rho_2$ are two $\ell$-adic Galois representations of the absolute Galois group of a number field, such that the algebraic monodromy group of one of the representations is connected and the representations are locally…

This paper continues the study of certain two-dimensional Galois representations attached to modular forms (mod p) via a construction due to Deligne. In particular, we prove a criterion for determining when the representation is split when…

Let K be a local field of mixed characteristic not absolutely ramified. Fontaine-Laffaille theory gives a description of the torsion crystalline Z_p-representations of the absolute Galois group of K (p denotes the characteristic of the…

We associate to a filtered $\varphi$-module $D$ a sub-$Z_p[[x]]$-module of convergent series on the open unit disk in which the $p$-adic $L$-functions of the Galois representation associated to $D$ and the $Z_p$-cyclotomic extension live…

Let $G$ be a $p$-divisible group over a complete discrete valuation ring $R$ of characteristic $p$. The generic fiber of $G$ determines a Galois representation $\rho$. The image of $\rho$ admits a ramification filtration and a Lie…

In this note we complement a part of a theorem of Fontaine-Mazur. We show that if $(V,\rho)$ is an irreducible finite dimensional representation of the Galois group $Gal({\bar K}/K)$ of a finite extension of $K\Q_p$, of Hodge-Tate type…

We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological…

We present several constraints on the absolute Galois groups G_F of fields F containing a primitive pth root of unity, using restrictions on the cohomology of index p normal subgroups from a previous paper by three of the authors. We first…

We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.

We classify 3-dimensional semistable Frob-semisimple representations of $G_{\mathbb{Q}_{p^{f}}}.$

Let p>2 be a prime, K a finite extension over Q_p and G :=Gal(\bar K/K). We extend Kisin's theory on \phi-modules of finite E(u)-height to give a new classification of G-stable Z_p-lattices in semi-stable representations

We consider limits of p-adic Galois representations, study different notions of convergence for such representations, and prove Cebotarev-type density theorems for them.

We propose in this paper an approach to Breuil's conjecture on a Langlands correspondence between $p$-adic Galois representations and representations of $p$-adic Lie groups in $p$-adic topological vector spaces. We suggest that Berthelot's…

For many finite groups, the Inverse Galois Problem can be approached through modular/automorphic Galois representations. This is a report explaining the basic strategy, ideas and methods behind some recent results. It focusses mostly on the…

Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in…

Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.

We give a complete classification of all the potentially crystalline 3-adic representations of the absolute Galois group of $\mathbb{Q}_3$ that are isomorphic to the Tate module of an elliptic curve defined over $\mathbb{Q}_3$. These…

I will survey some results in the theory of modular representations of a reductive $p$-adic group, in positive characteristic $\ell \neq p$ and $\ell=p$.

In this paper, we explicitly compute the semisimplifications of all Jacquet modules of irreducible representations with generic L-parameters of p-adic split odd special orthogonal groups or symplectic groups. Our computation represents them…

Let $k$ be an imaginary quadratic field and $p$ an odd prime number such that the $p$-rank of the class group of $k$ is one. Let $S$ be a finite set of places of $k$ distinct from $p$-adic places. We give sufficient conditions for the…