Jan Weidner
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Registered User
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19h |
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Weights on equivariant cohomology? For $f_*=f_!$ you are right, but only in the case where $f$ is a map between two $G$-varieties. However in the most interesting examples this is not the case! For example the relevant map for equivariant cohomology $X//G\rightarrow pt$ does NOT fit into this framework! |
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19h |
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Weights on equivariant cohomology? Thank you very much for your detailed discussion! By approxiamtions, I meant nice approximations, called "ABC" Olaf. Their most crucial property is, that they admit a nice stratification, such that the derived category of perverse sheaves equals the constructible derived category. It suffices to construct them for the group acting on a point and as you said, they are given by Stiefel varieties, if $G=GL_n$. Now the problem is, if you just take a subgroup of $GL_n$ and let it act on the Stiefel varieties, the resulting approximation won't be nice! |
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1d |
asked | Perverse sheaves for easy stratifications |
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1d |
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Weights on equivariant cohomology? I have looked into the other references you suggest and one thing I am missing (though it could be hidden somewhere, I don't understand them very well...) would be the formula $f_!=f_∗$ for proper $f$. Without it, I can't even deduce that $H_G(pt)$ is pure. Do you know if $f_!=f_∗$ is in there or follows easily? |
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1d |
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Weights on equivariant cohomology? Thanks for your comprehensive answer! One problem when working with approximations is, that you need to construct them. For example I would not know how to generalize O. Schnurer's thesis to the $P\G/Q$ case since I don't see how to construct the relevant approximations. Also approximations involve choices and choices usually lead to trouble in the long run. |
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Jun 11 |
asked | Weights on equivariant cohomology? |
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May 28 |
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Constructible derived category and fundamental category Yes, this is actually one of the proofs I had in mind, when I wrote I never intuitively understood the description. I find constructible sheaves = reps of the fundamental category very convincing. On the other hand Beilinson's glueing is quite intransparent to me. |
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May 27 |
asked | Constructible derived category and fundamental category |
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May 6 |
accepted | Has there been any application of tensor species? |
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May 4 |
awarded | ● Notable Question |
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Apr 30 |
awarded | ● Notable Question |
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Apr 25 |
revised |
A_infinity structure on cohomology and the weight filtration added 29 characters in body |
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Apr 24 |
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A_infinity structure on cohomology and the weight filtration Ok I better delete my nonsense comment before is causes confusion! |
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Apr 24 |
answered | A_infinity structure on cohomology and the weight filtration |
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Apr 24 |
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A_infinity structure on cohomology and the weight filtration Yes of course, you are right Jeffrey. |
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Apr 18 |
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Intersection of all normalizers It is not obvious, whether the product of two Hamiltonian groups is Hamiltonian. In fact it is wrong, according to the classification in the wikipedia article. |
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Apr 18 |
answered | Intersection of all normalizers |
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Feb 22 |
asked | Definition of derived category of a stack |
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Feb 8 |
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Nice algebraic approximations of classifying spaces Thanks for your answer anyway. An $SL_k$ bundle is a k dimensional vector bundle, along with a non vanishing section of its top exterior power right? In what kind of trivial bundle can we embed these? |
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Feb 8 |
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Nice algebraic approximations of classifying spaces I think that all these properties hold for flag varieties. In BGS 4.4.3. this is stated and proven for full flag varieties but as far as I see the proof works also for partial flag varieites. |
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Feb 8 |
asked | Nice algebraic approximations of classifying spaces |
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Feb 7 |
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Rep Theory Consequences of Bott--Weil--Borel I think one can regard the BWB theorem as a precursor of the Beilinson Bernstein localization theorem. The latter gives an equivalence between representations of the Lie algebra and D-modules on the flag variety. I think one can hardly overestimate the importance of the latter theorem. It allows to use a lot of geometric machinery to solve representation theoretic problems. For example it was a key ingredient in the original proof of the Kazhdan-Lusztig conjectures. |
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Feb 6 |
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Ring with three binary operations I think this answer contains an interesting perspective, +1. |
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Feb 3 |
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Analogues of D-modules and constructible sheaves Yes I know, that the functor from twisted D-modules to singular category O is not an equivalence. However I would also not expect the thing on the "constructible sheaves" side to be equivalent to category O. Also my question is not really representation theory, I only added this after Jim Humphreys question. So I think the flag manifold being affine for some TDOs is not part of the problem. |
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Feb 3 |
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Analogues of D-modules and constructible sheaves Thanks for your answer! However it is not yet quite what I am looking for! What I would prefer is some category of constructible sheaf like objects on $G/B$ and not some slightly different space. Is this possible? |
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Feb 3 |
revised |
Analogues of D-modules and constructible sheaves added 338 characters in body; edited title |
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Feb 3 |
revised |
Analogues of D-modules and constructible sheaves edited tags |
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Feb 2 |
asked | Analogues of D-modules and constructible sheaves |
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Dec 27 |
awarded | ● Yearling |
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Dec 23 |
awarded | ● Necromancer |
