Related papers: Tate classes, equivariant geometry and purity
Lecture notes. Introduction to the cohomology of algebras, Lie algebras, Lie bialgebras and quantum groups. Contains a new derivation of the classification of classical r-matrices in terms of deformation cohomology, and a calculation of the…
We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant form by means of twisted equivariant cohomology of the manifold. We apply…
For abelian varieties $A$, in the most interesting cohomology theories $H^* (A)$ is the exterior algebra of $H^1(A)$. In this paper we study a weak generalization of this in the case of arithmetic manifolds associated to orthogonal or…
The paper proposes and motivates a conjecture on the invariance of cohomological support loci under derived equivalence. It contains a proof in the case of surfaces, and explains further developments and consequences.
Tate cohomology was originally defined over finite groups. More recently, Avramov and Martsinkovsky showed how to extend the definition so that it now works well over Gorenstein rings. This paper improves the theory further by giving a new…
Review of localization in geometry: equivariant cohomology, characteristic classes, Atiyah-Bott formula, Atiyah-Singer equivariant index formula, Mathai-Quillen formalism
In open quantum systems, entanglement can vanish faster than coherence. This phenomenon is usually called sudden death of entanglement. In [M. O. Terra Cunha, New J. Phys. 9, 237 (2007)] a geometrical explanation was offered and a…
In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation…
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…
We prove that the first integral cohomology of pure mapping class groups of infinite type genus one surfaces is trivial. For genus zero surfaces we prove that not every homomorphism to $\mathbb{Z}$ factors through a sphere with finitely…
It is known that the semisimplicity of quantum cohomology implies the vanishing of off-diagonal Hodge numbers (Hodge--Tateness). We investigate which hyperplane sections of homogeneous varieties possess either of the two properties. We…
Toric orbifolds are a generalization of simplicial projective toric varieties. In this paper, we show that there is a resolution of singularities of a toric orbifold. In a different category, the class of quasi-contact toric manifolds…
This is an example on the cohomology of threefolds.
These are notes of my lectures at the summer school "Higher-dimensional geometry over finite fields" in Goettingen, June--July 2007. We present a proof of Tate's theorem on homomorphisms of abelian varieties over finite fields (including…
The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…
In this note we discuss some examples of non torsion and non algebraic cohomology classes for varieties over finite fields. The approach follows the construction of Atiyah-Hirzebruch and Totaro.
We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We give various extensions of these rules, some new and…
In this expository article we give a categorical definition of the integral cohomology ring of a stack. We show that for quotient stacks the categorical cohomology may be identified with equivariant cohomology. Via this identification we…
The purpose of this paper is to show that the third unramified cohomology with divisible coefficients of a smooth projective geometrically rational threefold over a finite field must vanish under $\Z_{\ell}$-exactness Hard Lefschetz…
We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the $L_{q,p}$-cohomology of these manifolds. Some applications to vanishing and non vanishing results in $L_{q,p}$-cohomology are…