Related papers: Differentials on the arc space
Essentials of sheaves are briefly presented, followed by related comments on presheaves, bundles, manifolds and singularities, aiming to point to their differences not only in their different formal mathematical structures, but also in the…
We use the theory of motivic integration for singular spaces to give a characterization of minimal log discrepencies in terms of the codimension of certain subsets of spaces of arcs. This is done for arbitrary pairs $(X,Y)$, with $X$ normal…
The theory of relative logarithmic jet spaces is developed for log schemes. With this theory the existence of bounds of intersection multiplicities of curves and divisors on certain log schemes is established. This result extends those of…
The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash…
We study the differential properties of generalized arc schemes, and geometric versions of Kolchin's Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.
In the last twenty years a number of papers appeared aiming to construct locally free replacements of the sheaf of principal parts for families of Gorenstein curves. The main goal of this survey is to present to the widest possible audience…
We extend the theory of fields/distributions developed the paper "A Feigin-Frenkel theorem with n singularities" to a general base scheme. In order to do so we introduce suitable notions of topological sheaves on schemes and study their…
We introduce and develop the theory of metric sheaves. A metric sheaf $\A$ is defined on a topological space $X$ such that each fiber is a metric model. We describe the construction of the generic model as the quotient space of the sheaf…
We formalize the concept of sheaves of sets on a model site by considering variables thereof, or motifs, and we construct functorially defined derived algebraic stacks from them, thereby eliminating the necessity to choose derived…
In this paper, we study the differential smoothness of 3-dimensional skew polynomial algebras and diffusion algebras.
The generalization of the n-dimensional cube, an n-dimensional chain, the exterior derivative and the integral of a differential n-form on it are introduced and investigated. The analogue of Stokes theorem for the differential space is…
There is an interplay between models, specified by variables and equations, and their connections to one another. This dichotomy should be reflected in the abstract as well. Without referring to the models directly -- only that a model…
In this notes we show how a problem regarding continued fractions of rational numbers, lead to several phenomena in number theory and dynamics, and eventually to the problem of shearing of divergent diagonal orbits in the space of adelic…
In their work, \cite{GR}, Gaitsgory and Rozenblyum introduce a derived version of the well-studied arc spaces of classical algebraic geometry. They observe that these derived spaces do not differ from their classical counterparts in the…
We define a class of quadratic differential algebras which are generated as differential graded algebras by the elements of an Euclidean space. Such a differential algebra is a differential calculus over the quadratic algebra of its…
We compute the Mather minimal log discrepancy via jet schemes and arc spaces for toric varieties and very general hypersurfaces.
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…
We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…
The notion of prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares the prolongation spaces with algebraic jet spaces…
The multiplicative and additive compounds of a matrix have important applications in geometry, linear algebra, and the analysis of dynamical systems. In particular, the $k$-compounds allow to build a $k$-compound dynamical system that…