Related papers: Vector spaces with a dense-codense generic submodu…

Let $R$ be a discrete valuation ring with field of fractions $K$ and residue field $k$ of characteristic $p>0$. Given a finite commutative group scheme $G$ over $K$ and a smooth projective curve $C$ over $K$ with a rational point, we study…

We consider a special configuration in which a finite group $A$ acts by automorphisms on the finite group $G$, and the semidirect product $GA$ acts on the vector space $V$ by linear transformations; and discuss the existence of the regular…

We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all…

Given a vector-space $~V~$ which is the tensor product of vector-spaces $A$ and $B$, we reconstruct $A$ and $B$ from the family of simple tensors $a{\otimes}b$ within $V$. In an application to quantum mechanics, one would be reconstructing…

Let $R$ be a commutative ring with identity and $G$ a graph. Extending generalized splines are a further extension of generalized splines by allowing vertex labels of $G$ to lie in varying modules rather than in a fixed ring $R$.…

Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, and $X$ an $R$--module. In this paper, for fixed integers $s, t$ and a finite $\fa$--torsion $R$--module $N$, we first study the membership of…

The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

We discuss a Nash-Moser/ KAM algorithm for the construction of invariant tori for {\em tame} vector fields. Similar algorithms have been studied widely both in finite and infinite dimensional contexts: we are particularly interested in the…

Let $\pi$ be a finite dimensional unitary representation of a group $G$ with a generating symmetric $n$-element set $S\subset G$. Fix $\vp>0$. Assume that the spectrum of $|S|^{-1}\sum_{s\in S} \pi(s) \otimes \overline{\pi(s)}$ is included…

This paper, the third in a series of eight introduces some of the basic concepts of the theory of extensors needed for our formulation of the differential geometry of smooth manifolds . Key notions such as the extension and generalization…

We construct a moduli space of stable pairs over a smooth projective variety, parametrizing morphisms from a fixed coherent sheaf to a varying sheaf of fixed topological type, subject to a stability condition. This generalizes the notion…

In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…

This paper is the first of a series aiming at proving rigorously the analyticity and the Borel summability of generic quartic bosonic and fermionic vector models (generalizing the O(N) vector model) in diverse dimensions. Both…

We construct new substantive examples of non-autonomous vector fields on 3-dimensional sphere having a simple dynamics but non-trivial topology. The construction is based on two ideas: the theory of diffeomorpisms with wild separatrix…

Integrable quantum field theories in 1+1 dimensions have recently become amenable to a rigorous construction, but many questions about the structure of their local observables remain open. Our goal is to characterize these local observables…

We extend some properties of a pair of ideals described in terms of Tor modules to any number of ideals, including the well-known rigidity property. Those extensions require the development of a homological theory for spectral sequences…

Vacuum structure of a quantum field theory is a crucial property. In theories with extended symmetries, such as supersymmetric gauge theories, the vacuum is typically a continuous manifold, called the vacuum moduli space, parametrized by…

In this article we study the behaviour of semistable principal $G$-bundles over a smooth projective variety $X$ under the extension of structure groups in positive characteristic. We extend some results of Ramanan-Ramanathan…

We discuss finite local extensions of quantum field theories in low space time dimensions in connection with categorical structures and the question of modular invariants in conformal field theory, also touching upon purely mathematical…