Related papers: Du th\'eor\'eme de d\'ecomposition \'a la Puret\'e…

In [7, Papadima and Suciu, When does the associated graded Lie algebra of an arrangement group decompose? Comment. Math. Helv. {\bf 81:4} (2006), 859--875] it is proved that the holonomy Lie algebra of an arrangement of hyperplanes through…

We give a characterization of decomposition theory in linear algebra.

We consider versions of the local duality theorem in $\mathbb{C}^n$. We show that there exist canonical pairings in these versions of the duality theorem which can be expressed explicitly in terms of residues of Grothendieck, or in terms of…

The problem of classification of decomposable (in the sense of Stormer) positive maps between matrix algebras is presented. We propose the new notion of "finite" version of decomposability ($k$-decomposabilty). The characterisation of…

This is a second part of alg-geom/9611015. We construct a natural hyperkaehler desingularization for all singular hyperkaehler varieties. The desingularization theorem was proven in alg-geom/9611015 under additional assumption of local…

A new generalization of the classical separate algebraicity theorem is suggested and proved.

The question is raised whether the unique decomposition of the physical Hilbert space, as emerging in the refined algebraic quantization of a constrained system, may be understood in terms of the old Klein-Gordon type quantization.

We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This…

We will present a novel elementary, self-contained, and explicit proof of the local Kronecker-Weber theorem. Apart from discrete valuation theory, it does not make use of any tools beyond those introduced in a second undergraduate course on…

We prove the existence of a local analytic Levi decomposition for analytic Poisson structures and Lie algebroids.

We give a framework to produce constructible functions from natural functors between categories, without need of a morphism of moduli spaces to model the functor. We show using the Riemann-Hilbert correspondence that any natural (derived)…

We intoduce a local version of the Jordan-Brouwer separation theorem and deduce some global statements, some of which may follow from known results, but the technique is new.

In this paper a new general approach is developed to construct and study Lebesgue type decompositions of linear operators $T$ in the Hilbert space setting. The new approach allows to introduce an essentially wider class of Lebesgue type…

The aim of this short note is to extend results by Denef and Loughran, Skorobogatov, Smeets concerning refinements of a conjecture of Colliot-Thelene. The problem is about giving necessary and sufficient conditions for morphisms of…

We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.

Recent work of Beben and Theriault on decomposing based loop spaces of highly connected Poincar\'e Duality complexes has yielded new methods for analysing the homotopy theory of manifolds. In this paper we will expand upon these methods,…

This is the first in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global confor- mal invariants"; these are defined to be conformally invariant integrals of geometric scalars.…

Several Lebesgue-type decomposition theorems in analysis have a strong relation to the operation called: parallel sum. The aim of this paper is to investigate this relation from a new point of view. Namely, using a natural generalization of…

We prove a Decomposition Theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, we construct a category…

These are the lecture notes based on earlier papers with some additional new results. New and simple proofs are given for local freeness theorem and the semipositivity theorem. A decomposition theorem for higher direct images of dualizing…