Related papers: The A-decomposability of the Singer construction

We study Lie algebroids in positive characteristic and moduli spaces of their modules. In particular, we show a Langton's type theorem for the corresponding moduli spaces. We relate Langton's construction to Simpson's construction of…

The Singer algebraic transfer is a fundamental homomorphism in algebraic topology, providing a bridge between the homology of classifying spaces and the cohomology of the Steenrod algebra $\mathcal{A}$, which forms the $E_2$-term of the…

We derive necessary and sufficient conditions for an ambiskew polynomial ring to have a Hopf algebra structure of a certain type. This construction generalizes many known Hopf algebras, for example U(sl2), U_q(sl2) and the enveloping…

For a finite $\mathbb{Z}$-algebra $R$, i.e., for a ring which is not necessarily associative or unitary, but whose additive group is finitely generated, we construct a decomposition of $R/{\rm Ann}(R)$ into directly indecomposable factors…

A complex hyperplane arrangement $\mathcal{A}$ is said to be decomposable if there are no elements in the degree 3 part of its holonomy Lie algebra besides those coming from the rank 2 flats. When this purely combinatorial condition is…

We prove irreducibility for the space of cyclic covers of fixed numerical type between smooth projective curves, and also for the space of cyclic covers of prime order and of fixed numerical-combinatorial type between moduli-stable…

We formulate a structural principle for finite $S_2$-objects: coherent $S_2$-sheaves and finitely generated graded $S_2$-modules decompose canonically according to the connected components in codimension $1$ of their support. This gives…

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We…

Let $P$ be a principal indecomposable module of a finite group $G$ in characteristic $2$ and let $\varphi$ be the Brauer character of the corresponding simple $G$-module. We show that $P$ affords a non-degenerate $G$-invariant quadratic…

Let \sF be a coherent rank 2 sheaf on a scheme Y \subset \proj{n} of dimension at least two. In this paper we study the relationship between the functor which deforms a pair (\sF,\sigma), \sigma \in H^0(\sF), and the functor which deforms…

For a generic degree d smooth map f: N^n -> M^n we introduce its "transverse fundamental group" \pi(f), which reduces to \pi_1(M) in the case where f is a covering, and in general admits a monodromy homomorphism \pi(f) -> S_{|d|};…

Fix $\mathbb Z/2$ is the prime field of two elements and write $\mathcal A_2$ for the mod $2$ Steenrod algebra. Denote by $GL_d:= GL(d, \mathbb Z/2)$ the general linear group of rank $d$ over $\mathbb Z/2$ and by $\mathscr P_d$ the…

We say that a tempered distribution $A$ belongs to the class $S^m(\Ge)$ on a homogeneous Lie algebra $\Ge$ if its Abelian Fourier transform $a=\hat{A}$ is a smooth function on the dual $\Ges$ and satisfies the estimates $$…

For a Lorentzian homogeneous space, we study how algebraic conditions on the isotropy group affect the geometry and curvature of the homogeneous space. More specifically, we prove that a Lorentzian locally homogeneous space is locally…

In this paper, nonholonomic gerbes will be naturally derived for manifolds and vector bundle spaces provided with nonintegrable distributions (in brief, nonholonomic spaces). An important example of such gerbes is related to distributions…

The aim of this article is to define and study a notion of unstable algebra over an operad that generalises the classical notion of unstable algebra over the Steenrod algebra. For this study we focus on the case of characteristic 2. We…

In this short note, we will show the following weak evidence of S. Lang conjecture over function fields. Let f : X ---> Y be a projective and surjective morphism of algebraic varieties over an algebraically closed field k of characteristic…

A finite generalized quadrangle $\cS$ is a Singer quadrangle if it has an automorphism group that acts sharply transitively on its points. In this paper, we introduce the notion of multipliers for a Singer quadrangle and study their basic…

Given a ring homomorphism $B \to A$, consider its centralizer $R = A^B$, bimodule endomorphism ring $S = \End {}_BA_B$ and sub-tensor-square ring $T = (A \o_B A)^B$. Nonassociative tensoring by the cyclic modules $R_T$ or ${}_SR$ leads to…

Any finite set of linear operators on an algebra $A$ yields an operator algebra $B$ and a module structure on A, whose endomorphism ring is isomorphic to a subring $A^B$ of certain invariant elements of $A$. We show that if $A$ is a…