Related papers: Triangulation of refined families

We prove the finiteness and compatibility with base change of the (phi,Gamma)-cohomology and the Iwasawa cohomology of arithmetic families of (phi,Gamma)-modules. Using this finiteness theorem, we show that a family of Galois…

Let X_d be the p-adic analytic space classifying the d-dimensional (semisimple) p-adic Galois representations of the absolute Galois group of Q_p. We show that the crystalline representations are Zarski-dense in many irreducible components…

We study the $p$-adic variation of triangulations over $p$-adic families of $(\varphi,\Gamma)$-modules. In particular, we study certain canonical sub-filtrations of the pointwise triangulations and show that they extend to affinoid…

We study the cohomology of families of $(\varphi,\Gamma)$-modules with coefficients in pseudoaffinoid algebras. We prove that they have finite cohomology, and we deduce an Euler characteristic formula and Tate local duality. We classify…

We apply the theory of families of (phi,Gamma)-modules to trianguline families as defined by Chenevier. This yields a new definition of Kisin's finite slope subspace as well as higher dimensional analogues. Especially we show that these…

The goal of this article is to construct explicitly a p-adic family of representations (which are dihedral representations), to construct their associated (phi,Gamma)-modules by writing down explicit matrices for phi and for the action of…

Berger and Colmez introduced a theory of families of overconvergent \'etale (Phi,Gamma)-modules associated to families of p-adic Galois representations over p-adic Banach algebras. However, in contrast with the classical theory of…

We generalize Breuil-Hellmann-Schraen's local model for the trianguline variety to certain points with non-regular Hodge-Tate weights. With the local models we are able to prove, under the Taylor-Wiles hypothesis, the existence of certain…

This paper concerns arithmetic families of $\varphi$-modules over reduced affinoid spaces. For such a family, we first prove that the slope polygons is lower semicontinuous around any rigid point. If the slope polygons are locally constant…

We prove that the Balmer spectrum of a tensor triangulated category is homeomorphic to the Zariski spectrum of its graded central ring, provided the triangulated category is generated by its tensor unit and the graded central ring is…

The aim of this article is to prove Zariski density of crystalline representations in the rigid analytic space associated to the universal deformation ring of a d-dimensional mod p representation of Gal(\bar{K}/K) for any d and for any…

We use the theory of trianguline $(\varphi,\Gamma)$-modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at $p$, including those with characteristic $p$ coefficients.…

Existence of superdecomposable pure-injective modules reflects complexity in the category of finite-dimensional representations over an algebra. Such an existence occurs when an algebra is non-domestic; a conjecture due to M. Prest. G.…

Trianguline representations are a certain class of p-adic representations of Gal(Qp^alg/Qp) like the crystalline, semistable and de Rham representations of Fontaine. Their definition involves the theory of (phi,Gamma)-modules. In this…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

For a crystalline p-adic representation of the absolute Galois group of Qp, we define a family of Coleman maps (linear maps from the Iwasawa cohomology of the representation to the Iwasawa algebra), using the theory of Wach modules. Let f =…

Let $T$ be a triangulation of a Riemann surface. We show that the 1-skeleton of $T$ may be oriented so that there is a global bound on the outdegree of the vertices. Our application is to construct extremal metrics on triangulations formed…

We generalize to the finite-slope setting several techniques due to Nekovar concerning the parity conjecture for self-dual motives. In particular we show that, for a $p$-adic analytic family, with irreducible base, of symplectic self-dual…

We describe a family of representations of $\pi_1(\Sigma)$ in PU(2,1), where $\Sigma$ is a hyperbolic Riemann surface with at least one deleted point. This family is obtained by a bending process associated to an ideal triangulation of…

Let $R$ be a commutative ring. A full additive subcategory $\C$ of $R$-modules is triangulated if whenever two terms of a short exact sequence belong to $\C$, then so does the third term. In this note we give a classification of…