2
votes
1answer
100 views

When does the filtration in the limit of the Leray spectral sequence split?

Let $\ell$ be a prime, and $k$ a field of characteristic $\ne \ell$. Let $f \colon X \to Y$ be a proper map of smooth projective $k$-varieties. The Leray spectral sequence says $$ E_{2}^{pq} = ...
4
votes
1answer
198 views

Hodge classes and Leray filtration

Let $f :X \to Y$ be a submersion between smooth projective varieties over $\mathbb{C}$ and let $\alpha \in Z^k(X)$ be an algebraic cycle of $X$. Is is true that for all odd numbers $p$ and $q$ such ...
0
votes
1answer
171 views

Spectral sequence for composition of global sections and tensor product of sheaves

Hi all, on the forum page http://www.groupsrv.com/science/about506648.html one can read the following (i cut out nonimportant parts): Question: Does anyone know any condition (non trivial) that ...
1
vote
2answers
238 views

Leray spectral sequence of the inclusion of an open subvariety

Let $X$ be a smooth variety over a field $k \subset \mathbb{C}$ and $Z$ a smooth subvariety. Let $U=X-Z$. I'm trying to understand what information do the Leray spectral sequences attached to the ...
2
votes
1answer
221 views

Leray spectral sequence for lowest weight part of a smooth morphism

Let me assume everything in sight is as nice as possible, probably if the result I want is true then these conditions are too restrictive. All spaces will be smooth algebraic varieties over the ...
0
votes
0answers
242 views

spectral sequence of cohomology with compact support

Let k be a field, and A, B is subscheme of C over k, F is a sheaf over C. Question 1. what is the relation between $H_c(A\cap B,k)$, $H_c(B,F)$, and $H_c(A\cap B,F)$ ? Question 2. Let A be a strata ...
6
votes
2answers
683 views

How does one view the De Rham spectral sequence as a Grothendieck spectral sequence?

I was rereading basic results on de Rham cohomology, and this led me inevitably to the fact that $H^q(X,\Omega^p)$ converges to $H^*(X)$ for any smooth proper variety (over any field). How does one ...
3
votes
1answer
551 views

Special case of Leray spectral sequence

I am looking for a reference for what is stated in Srinivasan's book "Representations of Finite Chevalley Groups", which is apparently a special case of Leray spectral sequence. I'll quote the ...
2
votes
2answers
413 views

Vanishing cohomology of line bundles on the Springer resolution

My question is regarding Broer's paper "Line bundles on the cotangent bundle of the flag variety" (see http://www.springerlink.com/content/t41418q436524515/). Given the Springer resolution, and its ...
5
votes
1answer
741 views

Natural morphism appearing in Grothendieck spectral sequence

Assume we are in the setting of the Grothendieck spectral sequence (Weibel, 5.8): $G : A \to B, F : B \to C$ are left exact functors such that $G$ sends injective objects to $F$-acyclic objects. Now ...
3
votes
1answer
1k views

Question about hypercohomology / spectral sequence of a complex of “almost-acyclic” sheaves

I have a very particular situation involving a (non-exact) complex $K$ of coherent sheaves on a nonsingular projective variety $X$, and I need to compute the hypercohomology of the complex. The ...