Search Results

I have a stupid (and somewhat vague) comment: in the 'abelian' cases the answer is usually 'yes' by trivial reasons. If you check some cocycle condition (of any natuer) on objects of some abelian cate …

Can one formulate those version of Weak Lefschetz that uses tubular neighbourhoods purely in terms of cohomology of (some) algebraic varieties? … I would be completely satisfied with cohomology with $Z/l^n Z$-coefficients i.e. etale cohomology. …

For any $c>0$ does there exist an object $C$ of Voevodsky's $DM^{eff}_-$ (over the field of complex numbers) such that for any $i\le c$ and any smooth variety $X$ the $i$-th singular cohomology of $X$ …

Is it true that all pure Hodge structures 'that come from geometry' (for example, the graded pieces of the weight filtration of the singular cohomology of varieties and motives) are polarized? …

Étale cohomology with support and functoriality). … Still, does there exist a method for "computing" this relative cohomology (preferably by relating to the cohomology of some $\mathbb{C}$-varieties)? …

, if $Y$ is singular then you surely don't have transversality and probably don't have the isomorphism in question (as far as I remember, the intersection homology of $X$ is isomorphic to its "usual" cohomology …

Unfortunately, I don't know how to compute the cohomology of my $S$; I only know that it has 'many holes' in it (i.e. it is 'very far from being projective'), and it is finite over a variety $X$ with $ …

subvarieties of $X$ of dimension $m$ (here $H^\ast$ is singular or etale cohomology)? Did anybody study this filtration (for fixed $X,i$, when $m$ varies) before? …

Is there such a statement known i.e. does there exist a conjectural description of the coniveau filtration for singular cohomology of a smooth non-proper variety over the field of complex numbers (in …

I don't think that you have an obstruction on the level of Brauer groups. If you have a Galois-stable element over $L$, then you can choose some values of local invariants for its lift over $K$ such t …

Indeed, the cohomology groups in question would be exactly the weight zero part of the singular cohomology of $H$ (considered as a sequence of mixed Hodge structures), whereas for $i<\operatorname{dim} … Does Artin's vanishing hold for '$E_2$-weight pieces' for (torsion) cohomology of affine varieties? …

algebraic varieties over a subfield $k$ of the field of complex numbers, can one define certain mixed Hodge modules with some $k$-structure that would be related with the $k$-structure on the De Rham cohomology …

There are plenty of examples of varieties whose singular cohomology with rational coefficients considered as a mixed Hodge structure does not decompose as the direct sum of its pure (weight) factors. … Yet if we consider the cohomology just as filtered vector spaces over rationals, such a decomposition certainly exist (for any variety). …

Let $A^\ast$ be an algebraic oriented cohomology theory (i.e. it is equipped with certain push-forwards for projective morphisms of smooth varieties over the base field $k$; see section 2 of http://www.math.uiuc.edu … It seems sufficient to prove the latter for $A^\ast$ being the algebraic cobordism (as defined by Levine and Morel), since this is the universal algebraic oriented cohomology theory. …

The first one is based on the conjecture that Weil cohomology theories should yield exact and conservative functors on the category of mixed motives. In the paper Hanamura M. … The second approach was proposed by Voevodsky himeslf (in his well-known letter to Beilinson); it is based on the idea that the 'mixed motivic cohomology' of a (smooth) affine variety should satisfy the …