Related papers: Absolute Poincar\'e duality in \'etale cohomology
The Tutte polynomial is a classical invariant, important in combinatorics and statistical mechanics. An essential feature of the Tutte polynomial is the duality for planar graphs G, $T_G(X,Y)\; =\; {T}_{G^*}(Y,X)$ where $G^*$ denotes the…
Fix a noetherian scheme S. For any flat map f: X->Y of separated essentially-finite-type perfect S-schemes we define a canonical derived-category map c(f):\H(X)->f^!\H(Y), the fundamental class of f, where \H(Z) is the (pre-)Hochschild…
It is well known that the Euler characteristic of the cohomology of a complex algebraic variety coincides with the Euler characteristic of its cohomology with compact support. An old result of G. Laumon asserts that a relative version of…
We give an explicit formula for the Deligne pairing for a proper and flat morphisms $f:X\to S$ of schemes, in terms of the determinant of cohomology. The whole construction is justified by an analogy with the intersection theory on…
We show that \'etale correspondences between ample groupoids induce homomorphisms of homology groups. To complement this we explore the module categories of ample groupoids. We construct an induction-restriction adjunction for subgroupoids,…
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincar\'e Duality) and the tautness of the foliation are closely related. If…
We establish a loop space decomposition for certain $CW$-complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of Poincar\'{e} duality complexes in which a loop of a product…
The recent result of Brown and Zhang establishing Poincare duality in the Hochschild (co)homology of a large class of Hopf algebras is extended to right coideal subalgebras over which the Hopf algebra is faithfully flat, and applied to the…
In this paper we develop homology and cohomology theories which play the same role for real projective varieties that Lawson homology and morphic cohomology play for projective varieties respectively. They have nice properties such as the…
Consider a morphism between connected locally Noetherian normal schemes. In this paper, we discuss when the sequence of the etale fundamental groups associated to the morphism is exact. Moreover, we give a characterization of when the…
We establish a partial extension of the Poincar\'e duality theorem of Jell-Rau-Shaw to tropical hypersurfaces arising from non-primitive triangulations. We introduce a notion of level of primitivity for triangulations of lattice polytopes…
The more important difference between Riemann and pseudo-Riemann manifolds is the metric signature and its theoretical consequences. The practical application for Physics Theories becomes often impossible due to the signature consequences.…
In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case.…
A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…
In this paper, we establish a Poitou-Tate's global duality for totally positive Galois cohomology. We illustrate this result in the case of the twisted module "\`a la Tate" $\mathbb{Z}_{2}(i)$, $i$ integer.
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
Theories with General Relativity as a sub-sector exhibit enhanced symmetries upon dimensional reduction, which is suggestive of ``exotic dualities''. Upon inclusion of time-like directions in the reductions one can dualize to theories in…
We prove a sheaf-theoretic derived-category generalization of Greenlees-May duality (a far-reaching generalization of Grothendieck's local duality theorem): for a quasi-compact separated scheme X and a "proregular" subscheme Z---for…
Given an effective Cartier divisor D with simple normal crossing support on a smooth and proper scheme X over a perfect field of positive characteristic p, there is a natural notion of de Rham-Witt sheaves on X with zeros along D. We show…
We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.