Related papers: Gerbes for the Chow
Chow varieties are a parameter space for cycles of a given variety of a given codimension and degree. We construct their analog for differential algebraic varieties with differential algebraic subvarieties, answering a question of Gao, Li…
Braided non-commutative differential geometry is studied. In particular we investigate the theory of (bicovariant) differential calculi in braided abelian categories. Previous results on crossed modules and Hopf bimodules in braided…
Recently, symmetric categorical groups are used for the study of the Brauer groups of symmetric monoidal categories. As a part of these efforts, some algebraic structures of the 2-category of symmetric categorical groups $\mathrm{SCG}$ are…
This paper explores the cohomology of linear cycle sets, focusing on extensions of a specific linear cycle set H by an abelian group I. We derive explicit formulas for the second cohomology group, which classifies these extensions, and…
We introduce an axiomatic framework for the parallel transport of connections on gerbes. It incorporates parallel transport along curves and along surfaces, and is formulated in terms of gluing axioms and smoothness conditions. The…
We give an explicit combinatorial description of the deformation theory of the Abelian category of (quasi)coherent sheaves on any separated Noetherian scheme $X$ via the deformation theory of path algebras of quivers with relations, by…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
We explicitly describe cycle-class maps c_H from motivic cohomology to absolute Hodge cohomology, for smooth quasi-projective and (some) proper singular varieties, and compute special cases of the latter. For smooth projective varieties, we…
We construct a cohomology theory using quasi-smooth derived schemes as generators and an analogue of the bordism relation using derived fibre products as relations. This theory has pull-backs along all morphisms between smooth schemes…
We give a formalism of arithmetic mixed sheaves including the case of arithmetic mixed Hodge structures, and show the nonvanishing of certain higher extension groups, and also the nontriviality of the second Abel-Jacobi map for zero cycles…
For a cellular variety $X$ over a field $k$ of characteristic 0 and an algebraic oriented cohomology theory $\hh$ of Levine-Morel we construct a filtration on the cohomology ring $\hh(X)$ such that the associated graded ring is isomorphic…
We define a filtration on the Chow groups of a smooth projective variety X over a field k by using the cycle map into continuous l-adic etale cohomology. The main theorem says that if k is a function field in one variable over a finite…
Let $f : X -> B$ be a projective surjective morphism between quasi-projective varieties. The goal of this paper is the study of the Chow groups of $X$ in terms of the Chow groups of $B$ and of the fibers of $f$. One of the applications…
Reporting on a computer--assisted search for nonpositively curved CW complexes of intermediate rank conducted some years ago. Not intended for publication.
Our main goal is to give a sense of recent developments in the (stable) rationality problem from the point of view of unramified cohomology and 0-cycles as well as derived categories and semiorthogonal decompositions, and how these…
In this paper we explore the link between the theory of sheaves on graphs and noncommutative geometry showing that many concepts and constructions in the latter can be generalized and enhanced using methods coming from the former. They…
We will show that the singular cohomology groups of a smooth quasi-projective complex variety relative to a normal crossing divisor can be described in terms of delta-admissible chains. Roughly speaking, a delta-admissible chain is a…
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…
The purpose of this contribution is to point out connections between recent ideas about gerbes and gerbal actions (as higher categorical extension of representation theory) and old discussion in quantum field theory on commutator anomalies,…
We show the cardinality of a particular nonabelian cohomology associated to cyclic division algebras is equal to a certain partition number. This computation helps us interpret the number of conjugacy classes of maximal tori defined over an…