Related papers: Relative crystalline representations and $p$-divis…

Let $p$ be a prime. Let $(R,\ideal{m})$ be a regular local ring of mixed characteristic $(0,p)$ and absolute index of ramification $e$. We provide general criteria of when each abelian scheme over $\Spec R\setminus\{\ideal{m}\}$ extends to…

Let $K$ be an absolutely unramified $p$-adic field. We establish a ramification bound, depending only on the given prime $p$ and an integer $i$, for mod $p$ Galois representations associated with Wach modules of height at most $i$. Using an…

We show that loci of crystalline representations of $G_K$ for $K/\mathbb{Q}_p$ an unramified extension are irreducible when the Hodge--Tate weights are fixed and sufficiently small. This was previously known for weights in the interval…

We study the possible weights of an irreducible 2-dimensional modular mod p representation of the absolute Galois group of F, where F is a totally real field which is totally ramified at p, and the representation is tamely ramified at the…

In this paper, we investigate abstract homomorphism from the special linear group over complete discrete valuation rings with finite residue field, such as the ring of p-adic integers, into the general linear group over the reals. We find…

We provide an answer to two questions of Fontaine (in the unramified case). First, we show that a limit of crystalline representations, of bounded Hodge-Tate weights, is itself crystalline. Second, we show that every admissible filtered…

Let K_{f} be the finite unramified extension of Q_{p} of degree f and E any finite large enough coefficient field containing K_{f}. We construct analytic families of \'etale (Phi,Gamma)-modules which give rise to families of crystalline…

Let $\rho_p$ be an $n$-dimensional non-critical semistable $p$-adic Galois representation of the absolute Galois group of $\mathrm{Q}_p$ with regular Hodge--Tate weights. Let $\mathrm{D}$ be the associated $(\varphi,\Gamma)$-module over the…

Suppose F=W(k)[1/p] where W(k) is the ring of Witt vectors with coefficients in algebraically closed field k of characteristic p>2. We construct integral theory of p-adic semi-stable representations of the absolute Galois group of F with…

Let p>2 be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fractional field of the Witt ring of k. Let G and H be finite flat commutative group schemes killed by p over O_K and…

Let $K/\mathbb{Q}_p$ be a finite extension. For all irreducible representations $\bar\rho: G_K \to G(\bar{\mathbb{F}}_p)$ valued in a general reductive group $G$, we construct crystalline lifts of $\bar\rho$ which are Hodge-Tate regular. We…

Let $\mathcal{O}_K$ be a complete discrete valuation ring of mixed characteristic $(0,p)$ with perfect residue field. We prove the existence of the Hodge-Newton filtration for $p$-divisible groups over $\mathcal{O}_K$ with additional…

Let $F$ be a local field over $\mathbf{Q}_p$ or $\mathbf{F}_p((t))$, and let $D$ be a central simple division algebra over $F$ of degree $d$. In the $p$-adic case, we assume $p>de+1$ where $e$ is the ramification degree over $\mathbf{Q}_p$;…

Let $K$ be an unramified extension of $\mathbb{Q}_p$ and $\rho\colon G_K \rightarrow \operatorname{GL}_n(\overline{\mathbb{Z}}_p)$ a crystalline representation. If the Hodge--Tate weights of $\rho$ differ by at most $p$ then we show that…

Let $\mathcal{T}$ be an $\mathcal{O}_K$-linear idempotent-complete, small smooth proper stable $\infty$-category, where $K$ is a finite extension of $\mathbb{Q}_p$. We give a Breuil-Kisin module structure on the topological negative cyclic…

Let $p$ be an odd prime. Let $\rho: G_F \to \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a Galois representation of a totally real field $F$. For a small partial weight one weight $(k,0)$, we prove that modularity of $\rho$ can be…

Let k be a perfect field, and K be a totally ramified extension of K_0 = Frac W(k) of degree e. To a semi-stable p-adic representation of G_K (the absolute Galois group of K), one can classicaly associate two polygons : the Hodge polygon et…

We study the relative algebraic closure $K$ of $\bar{\mathbb{F}}_p((t))$ inside $\bar{\mathbb{F}}((t^{\mathbb{Q}}))$. We show that the supports of elements in $K$ have order type strictly less than $\omega^\omega$. We also recover a theorem…

Given a continuous, odd, reducible and semi-simple $2$-dimensional representation $\bar\rho_0$ of $G_{\mathbb{Q},Np}$ over a finite field of odd characteristic $p$, we study the relation between the universal deformation ring of the…

For a smooth and proper scheme over an artinian local ring with ordinary reduction over the perfect residue field we prove - under some general assumptions - that the relative de Rham-Witt spectral sequence degenerates and the relative…