Related papers: Andersen-Filtrierung und harter Lefschetz

In this paper we study skeleta of residually tame coverings of a marked curve over a non-archimedean field. We first generalize a result by Liu and Lorenzini by proving a simultaneous semistable reduction theorem for residually tame…

For a coherent filtered D-module we show that the dual of each graded piece over the structure sheaf is isomorphic to a certain graded piece of the ring-theoretic local cohomology complex of the graded quotient of the dual of the filtered…

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our joint work with D.Nikshych. In particular,…

This paper shows that the cyclotomic quiver Hecke algebras of type $A$, and the gradings on these algebras, are intimately related to the classical seminormal forms. We start by classifying all seminormal bases and then give an explicit…

Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in…

Here we show that, given a finite homological system $({\cal P},\leq,\{\Delta_u\}_{u\in {\cal P}})$ for a finite-dimensional algebra $\Lambda$ over an algebraically closed field, the category ${\cal F}(\Delta)$ of $\Delta$-filtered modules…

We introduce and study certain deformations of Drinfeld quasi-modular forms by using rigid analytic trivialisations of corresponding Anderson's t-motives. We show that a sub-algebra of these deformations has a natural graduation by the…

We introduce the notion of $\lambda$-equivalence and $\lambda$-embeddings of objects in suitable categories. This notion specializes to $L_{\infty\lambda}$-equivalence and $L_{\infty\lambda}$-elementary embedding for categories of…

We continue the research of an extension $\widetilde{\mid}$ of the divisibility relation to the Stone-\v Cech compactification $\beta N$. First we prove that ultrafilters we call prime actually possess the algebraic property of primality.…

We study the Hodge filtrations of Schmid and Vilonen on unipotent representations of real reductive groups. We show that for various well-defined classes of unipotent representations (including, for example, the oscillator representations…

For a positively graded artin algebra $A=\oplus_{n\geq 0}A_n$ we introduce its Beilinson algebra $\mathrm{b}(A)$. We prove that if $A$ is well-graded self-injective, then the category of graded $A$-modules is equivalent to the category of…

We give a classification of semisimple and separable algebras in a multi-fusion category over an arbitrary field in analogy to Wedderben-Artin theorem in classical algebras. It turns out that, if the multi-fusion category admits a…

To a big n-tilting object in a complete, cocomplete abelian category A with an injective cogenerator we assign a big n-cotilting object in a complete, cocomplete abelian category B with a projective generator, and vice versa. Then we…

Auslander's formula shows that any abelian category C is equivalent to the category of coherent functors on C modulo the Serre subcategory of all effaceable functors. We establish a derived version of this equivalence. This amounts to…

Anderson modules form a generalization of Drinfeld modules and are commonly understood as the counterpart of abelian varieties but with function field coefficients. In an attempt to study their ``motivic theory'', two objects of semilinear…

There are several interesting filtrations on the Cartan subalgebra of a complex simple Lie algebra coming from very different contexts: one is the principal filtration coming from the Langlands dual, one is coming from the Clifford algebra…

This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a\vee b in the section [b,1] is denoted by a\rightarrow b and can be considered as the connective…

In this paper we give a sum formula for the radical filtration of generalized Verma modules in any (possibly singular) blocks of parabolic BGG category which can be viewed as a generalization of Jantzen sum formula for Verma modules in the…

We introduce the notion of interlaced weak ditalgebras and apply reduction procedures to their module categories to prove a tame-wild dichotomy for the category ${\cal F}(\Delta)$ of $\Delta$-filtered modules for an arbitrary finite…

For any additive functor from modules (or, more generally, from an abelian category with enough projectives or injectives), we construct long sequences tying up together the derived functors, the satellites, and the stabilizations of the…