Related papers: Universal Deformation Rings for Complexes over Fin…

Consider the semisimple mod p reduction of the Galois representation associated to a Hilbert newform f by Carayol and Taylor. This paper discusses how, under certain conditions on f, the universal ring for deformations of this residual…

We study graded and ungraded singularity categories of some commutative Gorenstein toric singularities, namely, Veronese subrings of polynomial rings, and Segre products of some copies of polynomial rings. We show that the graded…

A vertex algebra with an action of a group $G$ comes with a notion of $g$-twisted modules, forming a $G$-crossed braided tensor category. For a Lie group $G$, one might instead wish for a notion of $(\mathrm{d}+A)$-twisted modules for any…

Let $R$ be a commutative ring and $\Gamma$ be an infinite discrete group. The algebraic $K$-theory of the group ring $R[\Gamma]$ is an important object of computation in geometric topology and number theory. When the group ring is…

The purpose of this paper is to prove dimension formulas for $T^1$ and $T^2$ for rational surface singularities. These modules play an important role in the deformation theory of isolated singularities in analytic and algebraic geometry.…

To every finite-dimensional $\mathbb C$-algebra $\Lambda$ of finite representation type we associate an affine variety. These varieties are a large generalization of the varieties defined by "$u$ variables" satisfying "$u$-equations", first…

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized…

We give a universal approach to the deformation-obstruction theory of objects of the derived category of coherent sheaves over a smooth projective family. We recover and generalise the obstruction class of Lowen and Lieblich, and prove that…

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geq 0$ and let $V$ be an irreducible rational $G$-module with highest weight $\lambda$. When $V$ is self-dual, a basic question to ask…

Based on our previous work on an arithmetic analogue of Christol's theorem, this paper studies in more detail the structure of the lambda-ring $E_K = K \otimes W_{O_K}^a (O_{\bar{K}})$ of algebraic Witt vectors for number fields $K$. First…

Let $R$ be an associative ring with unity $1$ and consider $k\in \mathbb{N}$ such that $1+1+..+1=k$ is invertible. Denote by $\omega$ an arbitrary kth root of unity in $R$ and let $UT^{(k)}_{\infty}(R)$ be the group of upper triangular…

We prove the statement/conjecture of M. Kontsevich on the existence of the logarithmic formality morphism. This question was open since 1999, and the main obstacle was the presence of $dr/r$ type singularities near the boundary $r=0$ in the…

Fix a finite field $\mathbb{F}$. Let $\mathrm{VI}$ be a skeleton of the category of finite dimensional $\mathbb{F}$-vector spaces and injective $\mathbb{F}$-linear maps. We study $\mathrm{VI}^m$-modules over a noetherian commutative ring in…

A well known result of B. Mazur gives a lower bound for the Krull dimension of the universal deformation ring associated to an absolutely irreducible residual representation in terms of the group cohomology of the adjoint representation.…

Let $\mathcal C$ be a class of modules over a ring $R$, closed under direct sums over index sets of cardinality $\kappa$ and isomorphisms, and such that the isomorphism classes form a set. The monoid of modules $V(\mathcal C)$ encodes the…

Let $K$ be a differential field over $\C$ with derivation $D$, $G$ a finite linear automorphism group over $K$ which preserves $D$, and $K^G$ the fixed point subfield of $K$ under the action of $G$. We show that every finite-dimensional…

We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…

Suppose a Lie group $G$ acts on a vertex algebra $V$. In this article we construct a vertex algebra $\tilde{V}$, which is an extension of $V$ by a big central vertex subalgebra identified with the algebra of functionals on the space of…

We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes $Z^\bullet$ of modules for a profinite group $G$ over a complete local Noetherian ring $A$ of positive residue characteristic…

This note intertwines the concepts of degeneration and contraction of algebras and quadratic forms defined on a vector space V . The general linear group GL(V ) acts regularly on the spaces of these two objects. The base field is taken to…