相关论文: Differentials over differential fields

The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-differential algebra with a weight, in analogy to the…

There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…

The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to algebraic curves.

We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…

We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples…

We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining…

A constructive approach to differential calculus on quantum principal bundles is presented. The calculus on the bundle is built in an intrinsic manner, starting from given graded (differential) *-algebras representing horizontal forms on…

We consider the local analytic behavior for a family of holomorphic differentials on a family of degenerating annuli. Three results and discussion are presented. The first is the normal families Lemma 1. The second is an isomorphism of…

In the prequel to this paper, two versions of Le Potier's strange duality conjecture for sheaves over abelian surfaces were studied. A third version is considered here. In the current setup, the isomorphism involves moduli spaces of sheaves…

Chow varieties are a parameter space for cycles of a given variety of a given codimension and degree. We construct their analog for differential algebraic varieties with differential algebraic subvarieties, answering a question of Gao, Li…

Normal affine algebraic varieties in characteristic 0 are uniquely determined (up to isomorphism) by the Lie algebra of derivations of their coordinate ring. This is not true without the hypothesis of normality. But, we show that (in…

We consider the algebra of Hecke correspondences (elementary transformations at a single point) acting on the algebraic K-theory groups of the moduli spaces of stable sheaves on a smooth projective surface S. We derive quadratic relations…

Inspired by several works on jet schemes and motivic integration, we consider an extension to singular varieties of the classical definition of discrepancy for morphisms of smooth varieties. The resulting invariant, which we call Jacobian…

We characterize those varieties of universal algebras where every split epimorphism considered as a map of sets is a product projection. In addition we obtain new characterizations of protomodular, unital and subtractive varieties as well…

Given a differential equation on a smooth fibre bundle Y, we consider its canonical vertical extension to that, called the deviation equation, on the vertical tangent bundle VY of Y. Its solutions are Jacobi fields treated in a very general…

The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in…

We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to results of the inverse theory in the calculus of…

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…

The paper sets out a generalized framework for Fourier-Mukai transforms and illustrates their use via vector bundle transforms. A Fourier-Mukai transform is, roughly, an isomorphism of derived categories of (sheaves) on smooth varieties X…

By analogy with algebraic geometry, we define a category of non-linear sheaves (quasi-coherent homotopy-sheaves of topological spaces) on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising…