Related papers: Versal deformations of formal arcs

The aim of this article is to give a rigorous geometric interpretation of the completion of a ring with respect to an ideal. To this end, we define the infinitesimal neighbourhood of an immersion of formal schemes as the largest possible…

We study groups of formal diffeomorphisms in several complex variables. For abelian, metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential forms which exhibit an invariance…

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.…

Let $X$ be a variety over a complete nontrivially valued field $K$. We construct an algebraizable formal model for the analytification of $X$ in the case $X$ admits a closed embedding into a toric variety. By algebraizable we mean that the…

We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…

Let $X$ be an integral scheme of finite presentation over a perfect field. Let $q$ be a singular closed point of $X$. We prove that there exists an open subset $V$ of $X$ containing $q$ such that $V$ admits a resolution, that is, there…

Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…

This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…

Given a fibration over the circle, we relate the eigenspace decomposition of the algebraic monodromy, the homological finiteness properties of the fiber, and the formality properties of the total space. In the process, we prove a more…

We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence…

We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…

We develop the notion of deformation of a morphism in a left-proper model category. As an application we provide a geometric/homotopic description of deformations of commutative (non-positively) graded differential algebras over a local…

We exhibit a smooth complex rational affine surface with uncountably many nonisomorphic real forms.

The strong homotopy Lie algebra, controlling simultaneous deformations of a morphism of associative algebras and its domain and codomain is constructed. Isomorphism of the cohomology of this strong homotopy Lie algebra with the classical…

We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…

We study when the derived intersection of two smooth subvarieties of a smooth variety is formal. As a consequence we obtain a derived base change theorem for non-transversal intersections. We also obtain applications to the study of the…

Given a lattice polytope Q in R^n, we define an affine scheme M(Q) that reflects the possibilities of splitting Q into a Minkowski sum. On the other hand, Q induces a toric Gorenstein singularity Y, and we construct a flat family over M(Q)…

We study derived intersections of smooth analytic cycles, and provide in some cases necessary and sufficient conditions for this intersection be formal. In particular, if X is a complex submanifold of a complex manifold Y, we prove that X…

We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…