Related papers: Refined intersection homology on non-Witt spaces
A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize \v{C}ech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\mathbb{P}^n_M$, a projective…
A homotopical treatment of intersection cohomology recently developed by Chataur-Saralegui-Tanr\'e associates a "perverse algebraic model" to every topological pseudomanifold, extending Sullivan's presentation of rational homotopy to…
This paper develops aspects of cosheaf theory on rigid analytic spaces, and demonstrates a sheaf-cosheaf Verdier duality equivalence theorem for overconvergent sheaves on separated, paracompact spaces, analogous to Jacob Lurie's treatment…
We extend the study of the de Rham operator with ideal boundary conditions from the case of isolated conic singularities, as analyzed by Cheeger, to the case of arbitrary stratified pseudomanifolds. We introduce a class of ideal boundary…
We present an obstruction theoretic inductive construction of intersection space pairs, which generalizes Banagl's construction of intersection spaces for arbitrary depth stratifications. We construct intersection space pairs for…
This paper investigates the Witt groups of triangulated categories of sheaves (of modules over a ring R in which 2 is invertible) equipped with Poincare-Verdier duality. We consider two main cases, that of perfect complexes of sheaves on…
Recent important and powerful frameworks for the study of differential forms by Huber-Joerder and Huber-Kebekus-Kelly based on Voevodsky's h-topology have greatly simplified and unified many approaches. This article builds towards the goal…
Banagl's method of intersection spaces allows to modify certain types of stratified pseudomanifolds near the singular set in such a way that the rational Betti numbers of the modified spaces satisfy generalized Poincar\'{e} duality in…
Cheeger-Simons differential characters and differential $K$-theory are refinements of ordinary cohomology theory and topological $K$-theory respectively, and they are examples of differential cohomology. Each of these differential…
This paper has two aims. The former is to give an introduction to our earlier work on the Hodge theory of algebraic maps and more generally to some of the main themes of the theory of perverse sheaves and to some of its geometric…
Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of…
We discuss a connection between coherent duality and Verdier duality via a Gersten-type complex of sheaves on real schemes, and show that this construction gives a dualizing object in the derived category, which is compatible with the…
Let $(M,g)$ be an incomplete Riemannian manifold of finite volume and let $2\leq p<\infty$. In the first part of this paper we prove that under certain assumptions the inclusion of the space of $L^p$-differential forms into that of…
Gerstenhaber and Schack ([GS]) developed a deformation theory of presheaves of algebras on small categories. We translate their cohomological description to sheaf cohomology. More precisely, we describe the deformation space of (admissible)…
This paper addresses the question: What is the de Rham theory for general differentiable spaces? We identify two potential answers and study them. In the first part, we show that the de Rham cohomology calculated using (the completion of)…
Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric…
We study sheaves on holomorphic spaces of loops and apply this to the study of the complex, defined in \cite{BdSHK}, governing deformations of the \emph{Poisson vertex algebra} structure on the space of holomorphic loops into a Poisson…
We examine Hopf cyclic cohomology in the same context as the analysis of the geometry of loop spaces $LX$ in derived algebraic geometry and the resulting close relationship between $S^1$-equivariant quasi-coherent sheaves on $LX$ and…
We look more closely at the higher nonabelian de Rham cohomology of a smooth projective variety or family of varieties that had been defined in some previous papers. We formalize using $n$-stacks the notion of shape underlying this…
We investigate the equivariant intersection cohomology of a toric variety. Considering the defining fan of the variety as a finite topological space with the subfans being the open sets (that corresponds to the "toric" topology given by the…