Related papers: Leveled sub-cohomology
We show that a smooth projective variety admits a Chow-Kunneth decomposition if the cohomology has level at most one except for the middle degree. This can be extended to the relative case in a weak sense if the morphism has only isolated…
In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case of locally…
We consider the category $\operatorname{Qcoh}\mathbb{X}$ of quasicoherent sheaves where $\mathbb{X}$ is a weighted noncommutative regular projective curve over a field $k$. This category is a hereditary, locally noetherian Grothendieck…
We prove that the cohomology algebra of elliptic arrangements depends only on the poset of layers. In the particular case of braid elliptic arrangements, we study the cohomology as representation and we compute some Hodge numbers. Finally,…
Let $Z'\subset \mathbb{P}^{n}$ be a smooth projective hypersurface of degree $d>1$ and let $Z\to \mathbb{P}^n$ be the $\mu_d$-cover totally ramified along $Z'$. We relate full level $d$ structures on the primitive cohomology $Z'$ with full…
In this very short note, we show that there is a relation between the leading term at $s=1$ of an $L$-function of an elliptic curve defined over an number field and the term that follows.
In the first part of this note, we review and compare various instances of the notion of twisted coefficient system, a.k.a. polynomial functor, appearing in the literature. This notion hinges on how one defines the degree of a functor from…
In this paper, we shall provide a purely $\infty$-categorical construction of the mixed graded structure over Chevalley-Eilenberg complexes computing homology and cohomology of Lie algebras defined over a field $\Bbbk$ of characteristic…
A theory of higher colimits over categories of free presentations is developed. It is shown that different homology functors such as Hoshcshild and cyclic homology of algebras over a field of characteristic zero, simplicial derived…
One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
For a monotone symplectic manifold and a smooth anticanonical divisor, there is a formal deformation of the symplectic cohomology of the divisor complement, defined by allowing Floer cylinders to intersect the divisor. We compute this…
A new category of topological spaces with additional structures, called m-towers, is introduced. It is shown that there is a covariant functor which establishes a one-to-one correspondences between unital (resp. arbitrary) subhomogeneous…
Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To abstract a continuum object hidden in the discrete surface, we…
On a smooth projective variety over the complex numbers, there is the coniveau from the coniveau filtration, which is called geometric coniveau. On the same variety, there is another coniveau from the maximal sub-Hodge structure, which is…
There is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces. We investigate symplectic aspects of this relationship, with a view to applications in low-dimensional…
One of the essential tasks in connectomics is the morphology analysis of neurons and organelles like mitochondria to shed light on their biological properties. However, these biological objects often have tangled parts or complex branching…
For any smooth projective variety with holomorphic locally homogeneous structure modelled on a homogeneous algebraic variety, we determine all the subvarieties of it which develop to the model.
We prove that E_n-homology of non-unital commutative algebras can be described as functor homology when one considers functors from a certain category of planar trees with n levels. For different n these homology theories are connected by…
Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from…