Related papers: Jets and differential linear logic

We construct a monoidal model structure on the category of all curved coalgebras and show that it is Quillen equivalent, via the extended bar-cobar adjunction, to another model structure we construct on the category of curved algebras. When…

Consider a subgroup of finite index of modular group. We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian of the corresponding modular curve. By BelyI theorem, such a criterion would apply to any curve over a…

For a linear algebraic group $G$ over a field $k$, we define an equivariant version of the Voevodsky's motivic cobordism $MGL$. We show that this is an oriented cohomology theory with localization sequence on the category of smooth…

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

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 continue work of our earlier paper (Lewitzka and Brunner: Minimally generated abstract logics, Logica Universalis 3(2), 2009), where abstract logics and particularly intuitionistic abstract logics are studied. Abstract logics can be…

We investigate under which assumptions a subclass of flat quasi-coherent shea\-ves on a quasi-compact and semi-separated scheme allows to "mock" the homotopy category of projective modules. Our methods are based on module theoretic…

The famous Erlangen Programme was coined by Felix Klein in 1872 as an algebraic approach allowing to incorporate fixed symmetry groups as the core ingredient for geometric analysis, seeing the chosen symmetries as intrinsic invariance of…

In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely…

We give a detailed proof that locally Noetherian moduli stacks of sections carry canonical obstruction theories. As part of the argument we construct a dualizing sheaf and trace map, in the lisse-etale topology, for families of tame twisted…

We define a filtration on the variational bicomplex according to jet order. The filtration is preserved by the interior Euler operator, which is not a module homomorphism with respect to the ring of smooth functions on the jet space.…

In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as $K$-theoretic versions of the Donaldson invariants. In…

The fourth paper of our series of papers entitled "Differential Geometry of Microlinear Frolicher Spaces is concerned with jet bundles. We present three distinct approaches together with transmogrifications of the first into the second and…

We study derivations and differential forms on the arithmetic jet spaces of smooth schemes, relative to several primes. As applications we give a new interpretation of arithmetic Laplacians and we discuss the de Rham cohomology of some…

This article studies the scheme structure of the jet schemes of determinantal varieties. We show that in general, these jet schemes are not irreducible. In the case of the determinantal variety $X$ of $r \times s$ matrices of rank at most…

In this paper we introduce a noncommutative analogue of the notion of linear system, which we call a helix $\underline{\mathcal{L}} := (\mathcal{L}_{i})_{i \in \mathbb{Z}}$ in an abelian category ${\sf C}$ over a quadratic…

Let G/Q be an homogeneous variety embedded in a projective space P thanks to an ample line bundle L. Take a projective space containing P and form the cone X over G/Q, we call this a cone over an homogeneous variety. Let $\alpha$ a class of…

Let $X$ be a smooth irreducible projective curve of genus $g \geq 2$ over a finite field $\F_{q}$ of characteristic $p$ with $q$ elements such that the function field $\F_{q}(X)$ is a geometric Galois extension of the rational function…

This paper is the sequel to our previous paper (Differetial Geometry of Microlinear Frolicher spaces IV-1), where three approaches to jet bundles are presented and compared. The first objective in this paper is to give the affine bundle…

Reconstructing jets, which provide vital insights into the properties and histories of subatomic particles produced in high-energy collisions, is a main problem in data analyses in collider physics. This intricate task deals with estimating…