Related papers: A family of acyclic functors

For a nice-enough category $\mathcal{C}$, we construct both the morphism category ${\rm H}(\mathcal{C})$ of $\mathcal{C}$ and the category ${\rm mod}\mbox{-}\mathcal{C}$ of all finitely presented contravariant additive functors over…

We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…

A description of the derived functors of Lie functors for free abelian groups is given.

We construct the reduction of an exact category with a twist functor with respect to an element of its graded center in presence of an exact-conservative forgetful functor annihilating this central element. The procedure allows, e.g., to…

We define and study a certain category of vector bundles on a p-adic curve to which we can associate in a functorial way finite dimensional p-adic representations of the geometric fundamental group. Among other things we investigate two…

We associate with a matrix over an arbitrary field an infinite family of matrices whose sizes vary from one to infinity; their entries are traces of powers of the original matrix. We explicitly evaluate the determinants of matrices in our…

Motivated in part by the study of the stable homology of automorphism groups of free groups, we consider cohomological calculations in the category $\mathcal{F}(\textbf{gr})$ of functors from finitely generated free groups to abelian…

Let E be a Frobenius category, let_E_ denote its stable category. The shift functor on_E_ induces a first shift functor on the category of acyclic complexes with entries in_E_ by pointwise application. Shifting a complex by 3 positions…

We introduce the primitivity of Fricke families, and give some examples. As its application, we first construct generators of the function field of the modular curve of level $N$ in terms of Fricke functions and Siegel functions,…

We study a family of surfaces of general type that arises from the intersections of two translates of the theta divisor on a principally polarized complex abelian fourfold. In particular we determine the N\'eron-Severi lattices of these…

Considering a (co)homology theory $\mathbb{T}$ on a base category $\mathcal{C}$ as a fragment of a first-order logical theory we here construct an abelian category $\mathcal{A}[\mathbb{T}]$ which is universal with respect to models of…

We consider families of cyclic covers of the projective line, where we fix the covering group and the local monodromies and we vary the branch points. We prove that there are precisely twenty such families that give rise to a special…

We study the homology of the dual de Rham complex as functors on the category of abelian groups. We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the…

Over any partially ordered abelian group whose positive cone is closed in an appropriate sense and has finitely many faces, modules that satisfy a weak finiteness condition admit finite primary decompositions. This conclusion rests on the…

We consider the coset poset associated with the families of proper subgroups, proper subgroups of finite index, and proper normal subgroups of finite index. We investigate under which conditions those coset posets have contractible…

We classify finite-dimensional complex Hopf algebras $A$ which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements $G(A)$ is abelian such that all prime divisors of the order…

We define two different simplicial complexes, the common divisor simplicial complex and the prime divisor simplicial complex, from a set of integers, and explore their similarities. We will define a map between the two simplicial complexes,…

We study aisles in the derived category of a hereditary abelian category. Given an aisle, we associate a sequence of subcategories of the abelian category by considering the different homologies of the aisle. We then obtain a sequence,…

We introduce and develop the notion of *displayed categories*. A displayed category over a category C is equivalent to "a category D and functor F : D --> C", but instead of having a single collection of "objects of D" with a map to the…

In this paper we define a functor-- leveled sub-cohomology. (It bears no relation with the level of elliptic curves). It is based on leveled cycles on a smooth projective variety, and will be expected to reveal a structure in the level.