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# Jan Weidner

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 Name Jan Weidner Member for 3 years Seen 13 hours ago Website Location Freiburg Age 25
 19h comment 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! 19h comment 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! 1d asked Perverse sheaves for easy stratifications 1d comment 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? 1d comment 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. Jun11 asked Weights on equivariant cohomology? May28 comment Constructible derived category and fundamental categoryYes, 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. May27 asked Constructible derived category and fundamental category May6 accepted Has there been any application of tensor species? May4 awarded ● Notable Question Apr30 awarded ● Notable Question Apr25 revised A_infinity structure on cohomology and the weight filtrationadded 29 characters in body Apr24 comment A_infinity structure on cohomology and the weight filtrationOk I better delete my nonsense comment before is causes confusion! Apr24 answered A_infinity structure on cohomology and the weight filtration Apr24 comment A_infinity structure on cohomology and the weight filtrationYes of course, you are right Jeffrey. Apr18 comment Intersection of all normalizersIt 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. Apr18 answered Intersection of all normalizers Feb22 asked Definition of derived category of a stack Feb8 comment Nice algebraic approximations of classifying spacesThanks 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? Feb8 comment Nice algebraic approximations of classifying spacesI 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. Feb8 asked Nice algebraic approximations of classifying spaces Feb7 comment Rep Theory Consequences of Bott--Weil--BorelI 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. Feb6 comment Ring with three binary operationsI think this answer contains an interesting perspective, +1. Feb3 comment Analogues of D-modules and constructible sheavesYes 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. Feb3 comment Analogues of D-modules and constructible sheavesThanks 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? Feb3 revised Analogues of D-modules and constructible sheavesadded 338 characters in body; edited title Feb3 revised Analogues of D-modules and constructible sheavesedited tags Feb2 asked Analogues of D-modules and constructible sheaves Dec27 awarded ● Yearling Dec23 awarded ● Necromancer