Related papers: Cohomological length functions
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation…
We study the categories of discrete modules for topological rings arising as the rings of operations in various kinds of topological K-theory. We prove that for these rings the discrete modules coincide with those modules which are locally…
We search for some splitting (resp. finiteness) criteria of a given module $M$ over a local ring $(R,\fm,k)$ in terms of the splitting (resp. finiteness) property of certain cohomological functors evaluated at $M$. In particular, we deal…
This first part of the paper describes the support of top graded local cohomology modules. As a corrolary one obtains a simple criteria for the vanishing of these modules and also the fact that they have finitely many minimal primes. The…
Some functorial and topological properties of vertical cohomologies and their application to completely integrable Hamiltonian systems are studied.
In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra…
We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality of separation and covering. We provide analogues for various geometric…
It is proved that the sum of the Loewy lengths of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result uncovers, in the structure of modules of finite projective…
In this paper we investigate homologically finite-dimensional objects in the derived category of a given small dg-enhanced triangulated category. Using these we define reflexivity, hfd-closedness, and the Gorenstein property for…
We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special K\"ahler geometry and…
This chapter sets out preliminaries for the duality theory in later chapters. An underlying idea is that local cohomology functors are higher derived functors of colocalizations (a.k.a.~coreflections). Predominantly well-known facts about…
In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher extensions - of objects in triangulated categories. These…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.
We want to compute generic $\mathrm{Ext}$-spaces of twisted polynomial functors in relation to the $\mathrm{Ext}$-spaces of the untwisted ones, modulo a parametrisation. Thanks to the study of a spectral sequence we get to a computation in…
We consider algebras defined over a complete, local and noetherian ground ring. They are gentle algebras in case the ground ring is a field. The unbounded homotopy category of complexes of projective modules is considered. Complexes with…
Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In…
The idea of transversality is explored in the construction of cohomology theory associated to regularized sequences of multiple products of rational functions associated to vertex algebra cohomology of codimension one foliations on complex…
The present paper studies structure of the ring of integer-valued entire functions. We characterize certain classes of prime and maximal ideals and investigate some of their properties.
The integral cohomology ring of the complement of an arrangement of linear subspaces of a finite dimensional complex projective space is determined by combinatorial data, i.e. the intersection poset and the dimension function.