Related papers: The Structure of $C^\infty$-Superschemes

Combining the Batchelor theorem and the Serre-Swan theorem, we come to that, given a smooth manifold $X$, a graded commutative $C^\infty(X)$-algebra $\cA$ is isomorphic to the structure ring of a graded manifold with a body $X$ iff it is…

A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize \v{C}ech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\mathbb{P}^n_M$, a projective…

We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying…

As an analogy of superalgebra of multivector fields with the Schounte bracket, we introduce a non-trivial superbracket on differential forms of manifold. We show properties of this new superalgebra. We extend this superalgebra by adding one…

In this article, we present a novel theory of locally semialgebraic superspaces along with Nash supermanifolds. By adapting Batchelor's theorem to our framework, we show that all locally semialgebraic superspaces and affine Nash…

We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…

The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The…

Grothendieck-Birkhoff Theorem states that every finite dimensional vector bundle over the projective line splits as the sum of one dimensional vector bundles. In this work we study simultaneous splittings of two dimensional vector bundles…

Extended geometry provides a unified framework for double geometry, exceptional geometry, etc., i.e., for the geometrisations of the string theory and M-theory dualities. In this talk, we will explain the structure of gauge transformations…

In this thesis we investigate a new formalism for supergeometry which focuses on the categorical properties of the theory. This approach is our main tool in the subsequent investigation of a global analytic approach to the construction of…

This study first provides a brief overview of the structure of typical Grassmann manifolds. Then a new type of supergrassmannians is construced using an odd involution in a super ringed space and by gluing superdomains together. Next,…

We show how a novel construction of the sheaf of Cherednik algebras on a quotient orbifold Y=X/G by virtue of formal geometry in author's prior work leads to results for the sheaf of Cherednik algebra which until recently were viewed as…

Grothendieck-Birkhoff Theorem states that every finite dimensional vector bundle over the projective line P1 splits as the sum of one dimensional vector bundles. This can be rephrased, in terms of orders, as stating that all maximal orders…

In this article, we prove that a free divisor in a three dimensional complex manifold must be Euler homogeneous in a strong sense if the cohomology of its complement is the hypercohomology of its logarithmic differential forms. F.J.…

In the first part of the paper we study the structure of Banach spaces with a conditional spreading basis. The geometry of such spaces exhibit a striking resemblance to the geometry of James' space. Further, we show that the averaging…

Let f: X -> Z be a separated essentially-finite-type flat map of noetherian schemes, and \delta: X --> X \times_Z X the diagonal map. The fundamental class C_f (globalizing residues) is a map from the relative Hochschild functor…

We define the characteristic cycle of a constructible sheaf on a smooth surface in the cotangent bundle. We prove that the intersection number with the 0-section equals the Euler number and that the total dimension of vanishing cycles at an…

We show that the K-theory cosheaf is a complete invariant for separable continuous fields with vanishing boundary maps over a finite-dimensional compact metrizable topological space whose fibers are stable Kirchberg algebras with rational…

We show that the $\infty$-category of global spaces is equivalent to the homotopy localization of the $\infty$-category of sheaves on the site of separated differentiable stacks, following a philosophy proposed by Gepner-Henriques. We…

The classical theory of Sobolev towers allows for the construction of an infinite ascending chain of extrapolation spaces and an infinite descending chain of interpolation spaces associated with a given $C_0$-semigroup on a Banach space. In…