Related papers: Dihedral Universal Deformations

In this article, we study the relation between the universal deformation rings and big Hecke algebras in the residually reducible case. Following the strategy of Skinner-Wiles and Pan's proof of the Fontaine-Mazur conjecture, we prove a…

We prove the existence of Euler systems for adjoint modular Galois representations using deformations of Galois representations coming from Hilbert modular forms and relate them to $p$-adic $L$-functions under a conjectural formula for the…

For a newform $f=\sum a_n q^n$ of weight $k \geq 3$ and a prime $\lambda$ of $\mathbf{Q}(a_n)$, the deformation problem for its associated mod $\lambda$ Galois representation is unobstructed for all primes outside some finite set. Previous…

We generalize the notion of semi-universality in the classical deformation problems to the context of derived deformation theories. A criterion for a formal moduli problem to be semi-prorepresentable is produced. This can be seen as an…

Let $k$ be a field of characteristic $p>0$, and let $W$ be a complete discrete valuation ring of characteristic $0$ that has $k$ as its residue field. Suppose $G$ is a finite group and $G^{\mathrm{ab},p}$ is its maximal abelian $p$-quotient…

A necessary condition for partial breaking of N=2 global supersymmetry is the presence of nonlinear deformations of the field transformations which cannot be generated by background values of auxiliary fields. This work studies the simplest…

A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…

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…

Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $\Lambda$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of…

Vogel's universality implies a unified description of the adjoint sector of representation theory for simple Lie algebras in terms of three parameters $\alpha,\beta,\gamma$, which are homogeneous coordinates of Vogel's plane. Actually this…

We study the twisted knot module for the universal deformation of an ${\rm SL}_2$-representation of a knot group, and introduce an associated $L$-function, which may be seen as an analogue of the algebraic $p$-adic $L$-function associated…

We consider deformations of finite or infinite dimensional Lie algebras over a field of characteristic 0. There is substantial confusion in the literature if one tries to describe all the non-equivalent deformations of a given Lie algebra.…

In this article, we prove the remaining open cases of the Fontaine-Mazur conjecture on two-dimensional regular Galois representations over $\Gal(\overline{\Q}/\Q)$ when $p=3$, hence concluding the conjecture in the regular case for all odd…

We introduce an $A_\infty$-algebra structure on the Hochschild cohomology of the endomorphism bimodule of a finite-dimensional representation of an associative algebra. We prove that this structure determines a presentation for…

In this work we compute the universal framed deformation functor for a reducible Galois representation $\rho$ given by direct sum of 2-dimensional representations $\rho_i$ coming from p-divisible groups. We impose the local conditions of…

We prove that the universal unramified deformation ring $R^{\mathrm{unr}}$ of a continuous Galois representation $\overline{\rho}: G_{F^{+}} \rightarrow \mathrm{GL}_n(k)$ (for a totally real field $F^{+}$ and finite field $k$) is finite…

The deformation theory of ordinary representations of the absolute Galois groups of totally real number fields (over a finite field $k$) has been studied for a long time, starting with the work of Hida, Mazur and Tilouine, and continued by…

We determine the universal deformation ring R(G,V) of certain mod 2 representations V of a finite group G which belong to a 2-modular block of G whose defect groups are isomorphic to a generalized quaternion group D. We show that for these…

We say that a two dimensional p-adic Galois representation of a number field F is weight two if it is de Rham with Hodge-Tate weights 0 and -1 equally distributed at each place above p; for example, the Tate module of an elliptic curve has…

We prove a Kuranishi-type theorem for deformations of complex structures on ALE K\"ahler surfaces. This is used to prove that for any scalar-flat K\"ahler ALE surface, all small deformations of complex structure also admit scalar-flat…