相关论文: Moduli stacks of \'etale (phi,Gamma)-modules and t…

We construct a moduli stack of rank 4 symplectic projective \'etale $(\varphi,\Gamma)$-modules and prove its geometric properties for any prime $p>2$ and finite extension $K/\mathbf{Q}_p$. When $K/\mathbf{Q}_p$ is unramified, we adapt the…

We studied framed deformations of two dimensional Galois representation of which the residue representation restrict to decomposition groups are scalars, and established a modular lifting theorem for certain cases. We then proved a family…

We construct and study the moduli of continuous representations of a profinite group with integral $p$-adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is…

In this paper we study deformations of mod $p$ Galois representations $\tau$ (over an imaginary quadratic field $F$) of dimension $2$ whose semi-simplification is the direct sum of two characters $\tau_1$ and $\tau_2$. As opposed to our…

We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, and relate their geometry to the weight part of Serre's conjecture for GL(2).

We study potentially crystalline deformation rings for a residual, ordinary Galois representation $\overline{\rho}: G_{\mathbb{Q}_p}\rightarrow \mathrm{GL}_3(\mathbb{F}_p)$. We consider deformations with Hodge-Tate weights $(0,1,2)$ and…

Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. We introduce the notion of crystalline $(\varphi,\Gamma)$-modules over $\widetilde{\mathbb{A}}_K^{+}$ and show that…

We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, as well as their resolutions by moduli stacks of two-dimensional Breuil-Kisin modules with tame descent data. We study…

Let $\Lambda$ be a complete noetherian local ring with finite residue field of characteristic $p$ and $K/\mathbb{Q}_p$ a $p$-adic field. We show that, by deformation of the structure sheaf on the (transversal) prismatic site of a bounded…

We develop a local model theory for moduli stacks of $2$-dimensional non-scalar tame potentially Barsotti--Tate Galois representations of the Galois group of an unramified extension of $\mathbb{Q}_p$. We derive from this explicit…

For a representation of the absolute Galois group of the rationals over a finite field of characteristic $p$, we study the existence of a lift to characteristic zero that is geometric in the sense of the Fontaine-Mazur conjecture. For…

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 determine semisimple reductions of irreducible, 2-dimensional crystalline representations of the absolute Galois group $\text{Gal}(\overline{\mathbb{Q}_p}/\mathbb{Q}_{p^f})$. To this end, we provide explicit representatives for the…

We study irreducible odd mod $p$ Galois representations $\bar{\rho} \colon \mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_p)$, for $F$ a totally real number field and $G$ a general reductive group. For $p \gg_{G, F} 0$, we show…

In this paper we study the universal lifting spaces of local Galois representations valued in arbitrary reductive group schemes when $\ell \neq p$. In particular, under certain technical conditions applicable to any root datum we construct…

We construct explicitly some analytic families of etale (phi,Gamma)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on…

We prove that both local Galois representations and $(\varphi,\Gamma)$-modules can be recovered from prismatic F-crystals, from which we obtain a new proof of the equivalence of Galois representations and $(\varphi,\Gamma)$-modules.

We adapt a technique of Kisin to construct and study crystalline deformation rings of $G_K$ for a finite extension $K/\mathbb{Q}_p$. This is done by considering a moduli space of Breuil--Kisin modules, satisfying an additional Galois…

We study G-valued Galois deformation rings with prescribed properties, where G is an arbitrary (not necessarily connected) reductive group over an extension of Z_l for some prime l. In particular, for the Galois groups of p-adic local…

For a rational prime $p \geq 3$ and an integer $n \geq 2$, we study the modularity of continuous 2-dimensional mod $p^n$ Galois representations of $\Gal(\bar{\Q}/\Q)$ whose residual representations are odd and absolutely irreducible. Under…