We consider correspondences on smooth quasiprojective varieties U . An algebraic cycle inducing the Künneth projector onto H(U) is constructed. Assuming normal crossings at infinity, the existence of relative motivic cohomology is shown to imply the independence of ` for traces of open correspondences.

We compute the completion of the groups SLn(Zt]) and SLn (Zt;t ?1 ]) relative to the obvious homomorphisms to SLn (Q); this is a generalization of the classical Malcev completion. We also make partial computations of the rational second cohomology of these groups.

We compute the completion of the groups SLn(Zt]) and SLn (Zt;t ?1 ]) relative to the obvious homomorphisms to SLn (Q); this is a generalization of the classical Malcev completion. We also make partial computations of the rational second cohomology of these groups.

let $r$ be a commutative noetherian ring with non-zero identity and $fa$ an ideal of $r$. let $m$ be a finite $r$--module of finite projective dimension and $n$ an arbitrary finite $r$--module. we characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(m,n)$ in certain serre subcategories of the category of modules from upper bounds. we define and study the properti...

In this note we explore the relationships between the motivic cohomology operations and the (classical) cohomology operations defined on mod-l étale cohomology. More precisely we show that the cohomology operations on motivic cohomology transform to the (classical) cohomology operations on mod-l étale cohomology upon inverting the motivic Bott element.

We show that the de Rham theorem, interpreted as the isomorphism between distributional de Rham cohomology and simplicial homology in the dual dimension for a simplicial decomposition of a compact oriented manifold, is a straightforward consequence of elementary properties of currents. The explicit construction of this isomorphism extends to other cases, such as relative and absolute cohomology...

In 1933, anticipating formal cohomology theory, van Kampen [5] gave a slightly rough description of an obstruction o(K) ∈ H Z/2(K ,Z) which vanishes if and only if an n-dimensional simplicial complex K admits a piecewise-linear embedding into R, n ≥ 3. Here K is the deleted product of a complex K. The cohomology in question is the Z/2-equivariant cohomology where Z/2 acts on the space by exchan...

We show that a smooth projective variety admits a Chow-Künneth decomposition if the cohomology has level at most one except for the middle degree. This can be extended to the relative case in a weak sense if the morphism has only isolated singularities, the base space is 1-dimensional, and the generic fiber satisfies the above condition.

Let X be a minuscule Schubert variety. In this article, we use the combinatorics of quivers to define new quasi-resolutions of X . We describe in particular all relative minimal models π̂ : X̂ → X of X and prove that all the morphisms π̂ are small (in the sense of intersection cohomology). In particular, all small resolutions of X are given by the smooth relative minimal models X̂ and we describe a...

We study the cohomology of Jacobians and Hilbert schemes points on reduced locally planar curves, which are however allowed to be singular reducible. show that cohomologies all subcurves encoded in fine compactified connected subcurves, via perverse Leray filtration. also prove, along way, a result independent interest, giving sufficient conditions for smoothness total space relative Jacobian f...