Related papers: Producing "new" semi-orthogonal decompositions in …

Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies…

We introduce arrangements of rational sections over curves. They generalize line arrangements on P^2. Each arrangement of d sections defines a single curve in P^{d-2} through the Kapranov's construction of \bar{M}_{0,d+1}. We show a…

There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here produce Helmholtz theorems for differential 1-forms and…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

We describe a bicategory $(\mathcal{R}ed\,\mathcal{O}rb)$ of reduced orbifolds in the framework of classical differential geometry (i.e. without any explicit reference to notions of Lie groupoids or differentiable stacks, but only using…

In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems,…

In this article we prove that all the inclusions between the 'classical' and naturally defined full triangulated subcategories of a weakly approximable triangulated category are intrinsic (in one case under a technical condition). This…

We introduce new enhancements for the bounded derived category $D^b(Coh(X))$ of coherent sheaves on a suitable scheme $X$ and for its subcategory $Perf(X)$ of perfect complexes. They are used for translating Fourier-Mukai functors to…

The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…

We present a new notion of decomposition of semialgebraic sets by introducing a mode of irreducibility based on arc-analytic functions. The result is a refinement of the decomposition of such sets with respect to the Zariski topology as…

Expository paper on the relations between perturbation theory of pseudo-differential operators, finiteness theorems and deformations of Lagrangian varieties.

Derived decompositions of abelian categories are introduced in internal terms of abelian subcategories to construct semi-orthogonal decompositions (or Bousfield localizations, or hereditary torsion pairs) in various derived categories of…

A digraph is semicomplete if any two vertices are connected by at least one arc and is locally semicomplete if the out-neighbourhood and the in-neighbourhood of any vertex induce a semicomplete digraph. In this paper we study various…

This paper is an MGM version of arXiv.org:1703.04266 and arXiv:1907.03364, and a follow-up to Section 5 of arXiv:1503.05523. In the setting of a commutative ring $S$ with a weakly proregular finitely generated ideal $J\subset S$, we…

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasi-classical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise…

We propose the notion of a supercategory as an alternative approach to supermathematics. We show that this setting is rich to carry out many of the basic constructions of supermathematics. We also prove generalizations of a number of…

Interest in Conformal Field Theories and Quantum Field Theory lead physicists to consider configuration spaces of marked points on the complex projective line, $Conf_{0,d}(\mathbb{P})$. In this paper, a real semi-algebraic stratification of…

We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of $\mathbb{R}^n$. In this framework, a CAD $\mathscr{C}$ is adapted to a given set $S$ if $S$ is a union of cells of $\mathscr{C}$.…

We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field. We obtain a new proof of the following result due to Xiao and Zhu: the…