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Aug
5
comment Is it possible to classify the indecomposable representations of the wild quiver with one vertex and two arrows using infinite sets of parameters?
You should also define what you mean by $\mathbb{F}_2$. I guess you mean the quiver with one vertex and two arrows?
Jul
27
comment Is there a structure theorem or group law for finite groups generated by two elements?
mathoverflow.net/questions/59213/…
Jul
15
comment Is there a topological Chevalley-Shephard-Todd Theorem?
So now we arrive at the converse, and Jason's argument. I agree there is something left to show...
Jul
15
comment Is there a topological Chevalley-Shephard-Todd Theorem?
@Nico: so now I think I understand better: the quotient $\mathbb{C}^n \to \mathbb{C}^n/\Gamma$ is a quotient both in the category of topological spaces, and algebraic varieties. In particular, if $\Gamma$ is generated by pseudoreflections then it will be a topological manifold after all (by classical Chevalley-Shephard-Todd).
Jul
15
comment Is there a topological Chevalley-Shephard-Todd Theorem?
@Nico: Sorry, I wrote that comment after a glass of wine.
Jul
14
comment Is there a topological Chevalley-Shephard-Todd Theorem?
I don't know why there is a bounty ... it seems Jason has already answered the question!
Apr
17
awarded  Enthusiast
Apr
5
comment Cohomology of a local system and Deligne's weight filtration
@use54343: What do you mean by "your construction"? Restricting $IC$ to a strata? Doesn't taking $\mathcal{L}$ to the the local system I describe (an $IC$) recover what you want. (It is not clear to me how your second paragraph relates to the first. It seems your question is simply a question about variations of mixed Hodge structures on $\mathbb{C}^*$ and their cohomology. It would be much clearer if stated in this way.)
Apr
4
comment Cohomology of a local system and Deligne's weight filtration
You are right to be suspicious. If one takes the direct image of the constant sheaf under $z \mapsto z^2$ one gets a local system which splits into two pieces, both of which are pure, and one of which has no cohomology. The non-trivial summand gives a counter-example to your hopes. Making $1 - f$ compatible with weight filtrations is a tricky business, in the mixed Hodge world it is given by the limit mixed Hodge structure...
Apr
3
comment Status of Borho and Brylinski's irreducibility conjectures?
@Webstermeister To be honest I don't see immediately why it is the same question...
Apr
2
comment Status of Borho and Brylinski's irreducibility conjectures?
This may or may not be relevant: front.math.ucdavis.edu/1405.3479 !
Feb
27
revised Residual finiteness: why do we care?
added 1 character in body
Dec
12
answered Example to show that the inverse image under a finite morphism is not t-exact with respect to the perverse t-structure
Dec
9
answered Representation of GL(n, F_p) over F_p, for n small
Dec
9
answered counting points on nilpotent Springer fiber
Dec
9
comment counting points on nilpotent Springer fiber
One should be a little careful here. De Concini, Lusztig and Procesi do not show the existence of an affine paving in exceptional type. Moreover I think that the argument with a torus having finitely many fixed points only works in type $A$.
Dec
3
awarded  Necromancer
Dec
2
revised Motivation behind the construction of Deligne and Lusztig
edited body
Dec
2
answered Motivation behind the construction of Deligne and Lusztig
Nov
24
comment Stability conditions of coherent sheaves on abelian 3-folds
there has recently been big progress here. See Maciocia, Piyaratne "Fourier-Mukai transforms and Bridgeland stability conditions on abelian threefolds" I and II and "The space of stability conditions for abelian threefolds, and some Calabi-Yau threefolds" by Beyer, Macri and Stellari. (I am not an expert and so could have missed an important reference, but you certainly should be aware of these papers.)