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Results tagged with perverse-sheaves
Search options questions only
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user 919
27
votes
0
answers
953
views
Nearby cycles without a function
Suppose that:
$X$ is a smooth complex algebraic variety,
$f : X \to D$ is a proper map to a small disc, smooth away from 0,
$Z_\epsilon = f^{-1}(\epsilon)$, and $Z = Z_0$.
Then there is a procedure …
- 6,162
15
votes
1
answer
2k
views
Gabber's original proof of his purity theorem
Gabber's purity theorem is the statement that if $\mathscr{F}$ is a pure perverse sheaf on an open subvariety $j : U \hookrightarrow X$ then so is $j_{!*} \mathscr{F}$.
It is remarkable because it gi …
- 6,162
14
votes
2
answers
935
views
Non semi-simple monodromy in an algebraic family
I am looking for an example of a (edit: projective) family
$f : X \to Y$
of complex algebraic varieties which is a topologically locally trivial fibration in (singular) varieties and such that there …
- 6,162
4
votes
1
answer
397
views
Decomposition of direct image of a smooth morphism, Deligne's theorem, motives
Let $f : X \to Y$ be projective and smooth morphism of complex algebraic varieties. Here we care about the algebraic topology of $X$ and $Y$, so use classical topology for simplicity.
I can take the c …
- 6,162