Related papers: Computation of Framed Deformation Functors

q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…

Let $p$ be a prime number and $F$ a totally real number field. For each prime $\mathfrak{p}$ of $F$ above $p$ we construct a Hecke operator $T_\mathfrak{p}$ acting on $(\mathrm{mod}\, p^m)$ Katz Hilbert modular classes which agrees with the…

Let $p\geq 5$ be a prime number, $\mathbb{F}$ a finite field of characteristic $p$ and let $\bar{\chi}$ be the mod-$p$ cyclotomic character. Let $\bar{\rho}:\operatorname{G}_{\mathbb{Q}}\rightarrow \operatorname{GL}_2(\mathbb{F})$ be a…

We compute presentations of crystalline framed deformation rings of a two dimensional representation $\bar{\rho}$ of the absolute Galois group of $\mathbb{Q}_p$, when $\bar{\rho}$ has scalar semi-simplification, the Hodge-Tate weights are…

In this paper, we classify all continuous Galois representations $\rho:\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})\to \mathrm{GL}_2(\overline{\mathbf{Q}}_p)$ which are unramified outside $\{p,\infty\}$ and locally induced at $p$, under…

We compute the deformation rings of two dimensional mod l representations of Gal(Fbar/F) with fixed inertial type, for l an odd prime, p a prime distinct from p and F/Q_p a finite extension. We show that in this setting (when p is also odd)…

Let $\rho$ f,$\lambda$ be the residual Galois representation attached to a newform f and a prime ideal $\lambda$ in the integer ring of its coefficient field. In this paper, we prove explicit bounds for the residue characteristic of the…

We study deformation theory of mod $p$ Galois representations of $p$-adic fields with values in generalised reductive group schemes, such as $L$-groups and $C$-groups. We show that the corresponding deformation rings are complete…

We determine the mod $p$ reductions of all two-dimensional semi-stable representations $V_{k,\mathcal{L}}$ of the Galois group of $\mathbb{Q}_p$ of weights $3 \leq k \leq p+1$ and $\mathcal{L}$-invariants $\mathcal{L}$ for primes $p \geq…

Let G be the absolute Galois group of a global field. Let r1 and r2 be two p-adic, finite dimensional representations of G. Then there exists a finite number of primes q such that if the characteristic polynomials of r1(Frob_q) and…

We prove the existence of a new structure on the first Galois cohomology of generic families of symplectic self-dual $p$-adic representations of $G_{\mathbb{Q}_p}$ of rank two (a local sign decomposition): a functorial decomposition into…

We prove that, on average, elliptic curves over Q have finitely many primes p for which they possess a p-adic point of order p. We include a discussion of applications to companion forms and the deformation theory of Galois representations.

In this paper, we prove, under a technical assumption, that any semi-direct product of a $p$-group $G$ with a group $\Phi$ of order prime to $p$ can appear as the Galois group of a tower of extensions $H/K/F$ with the property that $H$ is…

We describe a universal factorization for a functor with values in finite-dimensional measured algebras. More precisely we contruct the quantum automorphism group of this functor. This general recontruction result allows us to recapture a…

Let $X$ be a smooth connected algebraic curve over an algebraically closed field $k$. We study the deformation of $\ell$-adic Galois representations of the function field of $X$ while keeping the local Galois representations at all places…

In this paper we prove the following theorem. Let L/\Q_p be a finite extension with ring of integers O_L and maximal ideal lambda. Theorem 1. Suppose that p >= 5. Suppose also that \rho:G_\Q -> GL_2(O_L) is a continuous representation…

In this note we study the geometry of torsors under flat and finite commutative group schemes of rank p above curves in characteristic p and above relative curves over a complete discrete valuation ring of inequal characteristics. In bothe…

Let $F$ be a local non-Archimedean field with ring of integers $o$. Let $\bf X$ be a one-dimensional formal $o$-module of $F$-height $n$ over the algebraic closure of the residue field of $o$. By the work of Drinfeld, the universal…

Let $(\mathbb{T}_f,\mathfrak{m}_f)$ denote the mod $p$ local Hecke algebra attached to a normalised Hecke eigenform $f$, which is a commutative algebra over some finite field $\mathbb{F}_q$ of characteristic $p$ and with residue field…

We study obstructed deformation problems for two-dimensional residual Galois representations arising from weight~$2$ newforms of level~$N$. Using Poitou-Tate duality, we isolate local and global sources of obstructions and give concrete…