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Results tagged with perverse-sheaves
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user 12336
12
votes
Accepted
What's an example of an intersection cohomology sheaf whose stalks are pure but not pointwis...
Here is an example. Sorry it's so complicated. (There's probably a simpler one, but my mind works in complicated ways, it seems.)
Consider a Siegel modular threefold $U$, i.e., a Shimura
variety for …
- 1,576
8
votes
Accepted
Is there an easy proof of the fact that the intermediate image functor respects weights?
The proof in BBD is not that complicated, and it doesn't matter much whether $j$ is affine or not. It uses the three following facts :
If $f$ is a morphism of schemes, then $f_*$ sends a complex of …
- 1,576
6
votes
Accepted
Bad behaviour of perverse sheaves over 'general' bases?
The answer is very likely "yes", but you will need to put together some technical articles (and unpublished results) that may not have yet been put together. Here are the key ingredients, as I see it …
- 1,576
6
votes
Accepted
Which statements in section 5 of BBD will fail if we consider $\mathbb{Q}_l$-adic sheaves th...
I think that all the statements are true, except for 5.3.9 (ii). Remark 5.3.10 says that all the statements in 5 up to and including 5.3.8 are true for $\mathbb{Q}_\ell$-coefficients with the same pro …
- 1,576
5
votes
Accepted
Functoriality properties of the perverse $t$-structure for torsion (constructible complexes ...
If you want only $\mathbb{Z}/\ell\mathbb{Z}$ coefficients (not general $\mathbb{Z}/\ell^m\mathbb{Z}$), then there is only one middle perverse t-structure, which is good. The way the exactness properti …
- 1,576
4
votes
Accepted
Is it easy to define weights for $Q_l$-sheaves over finite type $Z[1/l]$-schemes?
The answer to the question in your title is, I think : "in general, no". The answer to your last question is : "well, it depends how you have defined the objects, and you will have to be very careful …
- 1,576