Related papers: Colength one deformation rings

This paper is a brief review of recent results on the concept of ``generalized $\tau$-function'', defined as a generating function of all the matrix elements in a given highest-weight representation of a universal enveloping algebra ${\cal…

The modularity of an elliptic curve $E/\mathbb Q$ can be expressed either as an analytic statement that the $L$-function is the Mellin transform of a modular form, or as a geometric statement that $E$ is a quotient of a modular curve…

We consider mod $p$ Hilbert modular forms for a totally real field $F$, viewed as sections of automorphic line bundles on Hilbert modular varieties in prime characteristic $p$. For a Hecke eigenform of arbitrary weight, we prove the…

The light-cone gauge approach to $T{\overline T}$ deformed models is generalised to models deformed by U(1) conserved currents $J^\alpha$, $\widetilde J^\alpha$, stress-energy tensor $T^\alpha{}_\beta$, and their various quadratic…

We consider the relation between affine Toda field theories (ATFT) and Landau-Ginzburg Lagrangians as alternative descriptions of deformed 2d CFT. First, we show that the two concrete implementations of the deformation are consistent once…

Let $\mathcal{D}$ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a rigid object $R$. Let $\Lambda=\operatorname{End}_{\mathcal{D}}R$ be the endomorphism algebra of $R$. We introduce the notion of mutation of maximal…

Let $R$ be a positively graded finitely generated $\textbf{k}$-domain with Krull dimension $d+1$. We show that there is a homogeneous valuation $\mathfrak{v}: R \setminus \{0\} \to \mathbb{Z}^d$ of rank $d$ such that the associated graded…

This article studies the first-order $p$-adic deformations of classical weight one newforms, relating their fourier coefficients to the $p$-adic logarithms of algebraic numbers in the field cut out by the associated projective Galois…

We describe noncommutative geometric aspects of twisted deformations, in particular of the spheres in Connes and Landi [8] and in Connes and Dubois Violette [7], by using the differential and integral calculus on these spaces that is…

Let $\mathfrak{X}$ be a smooth connected $p$-adic formal scheme. Based on the prismatic description of crystalline local systems, we prove an analogue of Fontaine's conjecture for torsion crystalline local systems on the generic fiber of…

We give a complete list of formal invariants for a large class of formal differential 1-forms $\w \in \Bbb C [[ x, y]]dx + \Bbb C [[ x, y]]dy$. \indent A $\hat{SL}$-equisingular deformation is an equireducible deformation which leaves…

We show that the Eigenvariety attached to Hilbert modular forms over a totally real field $F$ is smooth at the points corresponding to certain classical weight one theta series and we give a precise criterion for etaleness over the weight…

Let $Y$ be a compact Gorenstein analytic space with only isolated singularities and trivial dualizing sheaf. A recent paper of Imagi studies the deformation theory of $Y$ in case the singularities of $Y$ are weighted homogeneous and…

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…

Let \rho be a modulo p representation of the absolute Galois group of a totally real number field. Under the assumptions that \rho has large image and admits a low weight crystalline modular deformation we show that any low weight…

We develop a notion of formal groups in the filtered setting and describe a duality relating these to a specified class of filtered Hopf algebras. We then study a deformation to the normal cone construction in the setting of derived…

In recent work with Bhatt and Morrow, we defined a new integral p-adic cohomology theory interpolating between etale and de Rham cohomology. An unexpected feature of this cohomology is that in coordinates, it can be computed by a…

Inspired by Nakamura's work (arXiv:1305.0880) on $\epsilon$-isomorphisms for $(\varphi,\Gamma)$-modules over (relative) Robba rings with respect to the cyclotomic theory, we formulate an analogous conjecture for $L$-analytic Lubin-Tate…

We prove the equality of several $\tau$-recurrent sequences, which were first considered by Pellarin, and which have close connections to Drinfeld vectorial modular forms. Our result has several consequences: an $A$-expansion for the…

We study the locally analytic vectors in the completed cohomology of modular curves and determine the eigenvectors of a rational Borel subalgebra of $\mathfrak{gl}_2(\mathbb{Q}_p)$. As applications, we prove a classicality result for…