Related papers: On Adically Complete D-Modules in Characteristic Z…

The paper constructs an `exotic' algebraic 2-complex over the generalized quaternion group of order 28, with the boundary maps given by explicit matrices over the group ring. This result depends on showing that a certain ideal of the group…

Let $A$ be a commutative Noetherian ring containing a field of characteristic zero. Let $R= A[X_1, \ldots, X_m]$ be a polynomial ring and $A_m(A) = A \langle X_1, \ldots, X_m, \partial_1, \ldots, \partial_m \rangle$ be the $m^{th}$ Weyl…

Let $(R, \mathfrak{m})$ be a commutative Noetherian local ring with total quotient ring $K$. An $R$-module $M$ is called simple divisible, if $M$ is divisible $\neq 0$, but every proper submodule $0 \neq U \subsetneqq M$ is not divisible.…

Let $X$ be a proper homogeneous space for a connected algebraic group $G$ over an algebraically closed field. For locally closed smooth affine subvarieties $W,Z\subset X$, we show that \[ (-1)^{\dim X-\dim W+\dim Z}\chi(gW\cap Z)\geq 0 \]…

Let d1,...,dn be a strictly increasing sequence of integers. Boij and S\"oderberg [arXiv:math/0611081] have conjectured the existence of a graded module M of finite length over any polynomial ring K[x_1,..., x_n], whose minimal free…

Let $(\Omega,{\mathcal F},P)$ be a probability space and $L^0({\mathcal F})$ the algebra of equivalence classes of real-valued random variables defined on $(\Omega,{\mathcal F},P)$. A left module $M$ over the algebra $L^0({\mathcal…

In this paper we develop a theory of convexity for a free Abelian group M (the lattice of integer points), which we call theory of discrete convexity. We characterize those subsets X of the group M that could be call "convex". One property…

Fix a smooth projective curve over a field of characteristic zero and a finite set of punctures. Let G be a connected linear algebraic group. We prove that the moduli of G-bundles with logarithmic connections having fixed residue classes at…

We give sufficient conditions allowing one to build a C*-algebraic structure on a self-adjoint linear subspace of a C*-algebra in such a way that the subspace is naturally identified with the resulting C*-algebra via a completely positive…

An $R$-module $M$ is called absolutely self pure if for any finitely generated left ideal of $R$ whose kernel is in the filter generated by the set of all left ideals $L$ of $R$ with $L \supseteq$ ann $(m)$ for some $m \in M$, any map from…

We prove that coherent configurations can be represented as modules over Frobenius structures in the category of real nonnegative matrices. We generalize the notion of admissible morphism from association schemes to coherent configurations.…

This paper contains an elementary proof of the existence of the classical model structure on the category of unbounded DG-Lie algebras over a field of characteristic zero, with an emphasis on the properties of free and semifree extensions,…

Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. In order to model nondeterministic semantics, the power structures over directed spaces were defined through the form of free…

We show that locally acyclic cluster algebras have (at worst) canonical singularities. In fact, we prove that locally acyclic cluster algebras of positive characteristic are strongly F-regular. In addition, we show that upper cluster…

Let X be a smooth projective curve over an algebraically closed field k of characteristic p>0. In this paper we explore the relation between algebraic D-modules on the moduli space $Bun_n$ of vector bundles of rank n on X and coherent…

For a finitely-generated vertex operator algebra of central charge c, a locally convex topological completion is constructed. We construct on the completion a structure of an algebra over the operad of the c/2-th power of the determinant…

We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for…

The stack $\overline{\mathcal{M}}_{g,n}$ of stable curves and its coarse moduli space $\overline{M}_{g,n}$ are defined over $\mathbb{Z}$, and therefore over any field. Over an algebraically closed field of characteristic zero, Hacking…

This paper concerns analytic free maps. These maps are free analogs of classical analytic functions in several complex variables, and are defined in terms of non-commuting variables amongst which there are no relations - they are free…

Let k be an algebraically closed field of characteristic zero, D a locally nilpotent derivation on the polynomial ring k[X_1, X_2,X_3,X_4] and A the kernel of D. A question of M. Miyanishi asks whether projective modules over A are…