Related papers: Slightly degenerate categories and $\mathbb{Z}$-mo…

Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \to Y$ ramified over a divisor $Z \subset Y$. We construct semiorthogonal decompositions of $\mathrm{D^b}(X)$…

We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential…

This paper is on $\Gamma$-convergence for degenerate integral functionals related to homogenisation problems in the Heisenberg group. Here both the rescaling and the notion of invariance or periodicity are chosen in a way motivated by the…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

We construct certain non-degenerate maps and sets, mainly in the complex-analytic category. For example, we show that for every countable subset S in an irreducible complex space X there exists a holomorphic map from the unit disk to X such…

We study the cyclic $U(\mathfrak{gl}_n)$-module generated by the $l$-th power of the $\alpha$-determinant. When $l$ is a non-negative integer, for all but finite exceptional values of $alpha$, one shows that this cyclic module is isomorphic…

In this note we are interested in labelling the irreducible representations of non-semisimple specialisations of Hecke algebras of complex reflection groups. We will use category O for the rational Cherednik algebra and the KZ functor…

Let C be a fusion category which is an extension of a fusion category D by a finite group G. We classify module categories over C in terms of module categories over D and the extension data (c,M,a) of C. We also describe functor categories…

Cluster algebras are categorified by cluster categories, and $g$-vectors are categorified by the classic index with respect to cluster tilting subcategories. However, the recently introduced completed discrete cluster categories of Dynkin…

Let $V$ be an elementary abelian $2$-group and $X$ be a finite $V$-CW-complex. In this memoir we study two cochain complexes of modules over the mod2 Steenrod algebra $\mathrm{A}$, equipped with an action of $\mathrm{H}^{*}V$, the mod2…

We continue the analysis of the Modular Isomorphism Problem for $2$-generated $p$-groups with cyclic derived subgroup, $p>2$, started in [D. Garc\'ia-Lucas, \'A. del R\'io, and M. Stanojkovski. On group invariants determined by modular…

We study finite-rank left-translation invariant algebraic $D$-modules on complex affine algebraic groups. Using the standard description of these objects as left-invariant flat algebraic connections on the trivial vector bundle, modulo…

We establish an Eichler-Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted…

We classify generalized tilting modules and full exceptional sequences for the family of quasi-hereditary quotients of type A zig-zag algebras and for a related family of algebras. We also give a characterization of these quotients as…

A $G$-graded extension of a fusion category $\mathcal{C}$ yields a categorical action of $G$ on the center $Z(\mathcal C)$. If the extension admits a spherical structure, we provide a method for recovering its fusion rules in terms of the…

We define the notion of index-module for a couple of A-lattices in a vector space, A being a Dedekind ring. We apply this notion to prove by elementary means that a weak Gras conjecture (i.e for irreducible nontrivial Q-characters) holds…

We study monoidal categorifications of certain monoidal subcategories $\mathcal{C}_J$ of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures coincide and arise from the category of finite-dimensional…

We develop the theory of Hopf bimodules for a finite rigid tensor category C. Then we use this theory to define a distinguished invertible object D of C and an isomorphism of tensor functors ?^{**} and D tensor ^{**}? tensor D^{-1}. This…

This paper classifies all modular data of integral modular fusion categories up to rank 13. Furthermore, it also classifies all integral half-Frobenius fusion rings up to rank 12. We find that each perfect integral modular fusion category…

Categories of W*-bimodules are shown in an explicit and algebraic way to constitute an involutive W*-bicategory.