Related papers: On jets, extensions and characteristic classes I

Let $A$ be an algebra over an operad in a cocomplete closed symmetric monoidal category. We study the category of $A$-modules. We define certain symmetric product functors of such modules generalising the tensor product of modules over…

In this paper we study noncommutative plane curves, i.e. non-commutative k-algebras for which the 1-dimensional simple modules form a plane curve. We study extensions of simple modules and we try to enlighten the completion problem, i.e.…

Jets of modules over a commutative ring are well known to make up the representative objects of linear differential operators on these modules. In noncommutative geometry, jets of modules provide the representative objects only of a certain…

In this paper we construct the jet geometrical extensions of the KCC-invariants, which characterize a given second-order system of differential equations on the 1-jet space $J^1(R,M)$. A generalized theorem of characterization of our jet…

In this paper we define and study generalized Atiyah classes for quasi coherent sheaves relative to arbitrary morphisms of schemes. We use derivations and quasi coherent sheaves of left and right O-modules to define a generalized first…

We prove that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic. The exponential modality is modelled by composing the…

In this article we construct three infinite families of endofunctors $J_d^{(n)}$, $J_d^{[n]}$, and $J_d^n$ on the category of left $A$-modules, where $A$ is a unital associative algebra over a commutative ring $\mathbb{k}$, equipped with an…

Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…

We formulate a notion of jet bundles over a possibly noncommutative algebra $A$ equipped with a torsion free connection. Among the conditions needed for 3rd-order jets and above is that the connection also be flat and its `generalised…

We will use Watts's theorem together with Lenzing's characterization of finitely presented modules via commuting properties of the induced tensor functor in order to study commuting properties of Ext-covariant functors.

We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `reduced' versions of the notions of higher Fitting…

Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their…

We extend Atiyah's holomorphic jet bundle formalism to holomorphic vector bundles over noncommutative algebras endowed with a bigraded differential calculus truncated at bidegree $(1,1)$; we refer to such structures as noncommutative…

In this article one extends the classical theory of (intermediate) Jacobians to the "noncommutative world". Concretely, one constructs a Q-linear additive Jacobian functor J(-) from the category of noncommutative Chow motives to the…

Let kK be the path algebra of the Kronecker quiver and consider the category of finite dimensional right modules over kK (called Kronecker modules). We prove that extensions of Kronecker modules are field independent up to Segre classes, so…

We associate to each unital $C^*$-algebra $A$ a geometric object---a diagram of topological spaces representing quotient spaces of the noncommutative space underlying $A$---meant to serve the role of a generalized Gel'fand spectrum. After…

Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, and $X$ an $R$--module. In this paper, for fixed integers $s, t$ and a finite $\fa$--torsion $R$--module $N$, we first study the membership of…

Many analyses at the collider utilize the hadronic jets that are the footprints of QCD partons. These are used both to study the QCD processes themselves and increasingly as tools to study other physics, for example top mass reconstruction.…

This is a continuation of our previous paper 1502.01744. We examine a class of non-commutative algebras A that depend on an elliptic curve and a translation automorphism of it. They may be defined in terms of the 4-dimensional Sklyanin…

It is emphasized that equivalent definitions of connections on modules over commutative rings are not so in noncommutative geometry.