Related papers: On Deligne's category $\uRep^{ab}(S_d)$

We describe the image of the canonical tensor functor from Deligne's interpolating category $Rep(GL_{m-n})$ to $Rep(GL(m|n))$ attached to the standard representation. This implies explicit tensor product decompositions between any two…

We investigate objects in symmetric tensor categories that have simultaneously finite symmetric and finite exterior algebra. This forces the characteristic of the base field to be $p>0$, and the maximal degree of non-vanishing symmetric and…

An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with…

We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.

We introduce a generalization of the notion of a negligible morphism and study the associated tensor ideals and thick ideals. These ideals are defined by considering deformations of a given monoidal category $\mathcal{C}$ over a local ring…

We study the question when a category of ind-objects is abelian. Our answer allows a further generalization of the notion of weakly Tannakian categories introduced by the author. As an application we show that, under suitable conditions,…

We prove that the sectional category of the universal fibration with fibre X, for X any space that satisfies a well-known conjecture of Halperin, equals one after rationalization.

It is shown that every concretizable category can be fully embedded into the category of accessible set functors and natural transformations.

For a given family $(G_i)_{i \in \N}$ of finitely generated abelian groups, we construct a Dedekind domain $D$ having the following properties. \begin{enumerate} \item $\Pic(D) \cong \bigoplus_{i \in \N}G_i$. \item For each $i \in \N$,…

We classify braided extensions $C$ of a rank $2$ fusion category. The result shows that $C$ is tensor equivalent to a Deligne's tensor product of some known categories, except $C$ is slightly degenerate and generated by a…

Under some assumptions we prove that the Deligne tensor product of categories of constructible perverse sheaves on pseudomanifolds X and Y is the category of constructible perverse sheaves on X\times Y. The Deligne external tensor product…

We first prove Bosch-L\"utkebohmert-Raynaud's conjectures on existence of global N\'eron models of not necessarily semi-abelian algebraic groups in the perfect residue fields case. We then give a counterexample to the existence in the…

In the first chapter we present new results related on monomial ideals of Borel type. Also, we introduce a new class of monomial ideals, called $\de$-fixed ideals, which generalize the class of $p$-Borel ideals and we extend several results…

We develop theory and examples of monoidal functors on tensor categories in positive characteristic that generalise the Frobenius functor from \cite{Os, EOf, Tann}. The latter has proved to be a powerful tool in the ongoing classification…

We generalize Abel's classical theorem on linear equivalence of divisors on a Riemann surface. For every closed submanifold $M^d \subset X^n$ in a compact oriented Riemannian $n$--manifold, or more generally for any $d$--cycle $Z$ relative…

For a commutative ring $R$ and a weakly proregular ideal $I$, we prove a simple universal property of the category of $L_0$-complete $R$-modules: it is the smallest replete exact abelian subcategory of the category of $R$-modules which…

Let $R$ be a commutative noetherian ring. Denote by $D^-(R)$ the derived category of cochain complexes $X$ of finitely generated $R$-modules with $H^i(X)=0$ for $i\gg0$. Then $D^-(R)$ has the structure of a tensor triangulated category with…

We establish the universal properties of the bicategory of polynomials, considering both cartesian and general morphisms between these polynomials. A direct proof of these universal properties would be impractical due to the complicated…

A symmetric tensor category $\mathcal D$ over an algebraically closed field $k$ is incompressible if every tensor functor out of $\mathcal D$ is an embedding. E.g., the categories $Vec$ and $sVec$ of (super)vector spaces are incompressible.…

In this note we characterize, within the framework of the theory of finite set, those categories of graphs that are {\em algebraic universal} in the sense that every concrete category embeds in them. The proof of the characterization is…