Related papers: Arithmetic differential operators on a semistable …

We derive certain systems of differential equations for matrix elements of products and iterates of logarithmic intertwining operators among strongly graded generalized modules for a strongly graded conformal vertex algebra under suitable…

A host algebra of a (possibly infinite dimensional) Lie group $G$ is a $C^*$-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations $\pi \colon G \to \U(\cH)$. In this paper we present…

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg vertex operator algebras. In this paper we examine logarithmic intertwining operators associated with…

Let $p$ be a prime number, $V$ a discrete valuation ring of unequal caracteristics $(0,p)$, $G$ a smooth affine algebraic group over $Spec \,V$. Using partial divided powers techniques of Berthelot, we construct arithmetic distribution…

We prove the existence of noncrossed product and indecomposable division algebras over the function field of a smooth p-adic curve, especially when the curve does not admit a smooth model over Z_p. Thus we generalize arXiv 0907.0670. To…

Let $\underline{\mathcal F}$ be a $\tau$-sheaf. Building on previous work of Drinfeld, Anderson, Taguchi, and Wan, B\"ockle and Pink \cite{bp1} develop a cohomology theory for $\underline{\mathcal F}$. In \cite{boc1} B\"ockle uses this…

Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold…

We present an explicit expression of the cohomology complex of a constructible sheaf of abelian groups on the small \'etale site of an irreducible curve over an algebraically closed field, when the torsion of the sheaf is invertible in the…

We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are…

We investigate a class of non-quasi-homogeneous free divisors in the sense of Saito. These divisors are defined by equations of the form $D:= \{h=0\}$ on $\mathbb{C}^p$, where the polynomial $h$ is specific linear combination of monomials…

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the…

We show that the space of first-order deformations of an orthogonal (resp. symplectic) sheaf over a smooth projective scheme is the first hypercohomology space of a complex which is naturally constructed out of the orthogonal (resp.…

This work presents an exposition of both the internal structure of derived category of an abelian category D*(A) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented…

Given a polynomial $f$ with coefficients in a field of prime characteristic $p$, it is known that there exists a differential operator that raises $1/f$ to its $p$th power. We first discuss a relation between the `level' of this…

The purpose of this note is to give a short proof of a theorem of Koll\'ar that the derived direct image of the canonical sheaf splits into a sum of its cohomology sheaves. This is deduced from a stronger decomposition theorem for direct…

The main goal of this paper is to establish close relations among sheaves of modules on atomic sites, representations of categories, and discrete representations of topological groups. We characterize sheaves of modules on atomic sites as…

We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…

We propose the following principle to study pointed Hopf algebras, or more generally, Hopf algebras whose coradical is a Hopf subalgebra. Given such a Hopf algebra A, consider its coradical filtration and the associated graded coalgebra…

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 describe a differential graded Lie algebra controlling infinitesimal deformations of triples $(X,\mathcal{F},\sigma)$, where $\mathcal{F}$ is a coherent sheaf on a smooth variety $X$ over a field of characteristic 0 and $\sigma\in…