Geordie Williamson
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Registered User
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May 5 |
awarded | ● Self-Learner |
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May 1 |
accepted | Vanishing of !-restriction of constructible sheaves |
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Apr 30 |
answered | Vanishing of !-restriction of constructible sheaves |
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Apr 30 |
comment |
Algebraic Stratifications of $G$-varieties yes, this is true and Braden is the perfect person to ask as ulrich says! If all you want is that the categories are preserved by the six operations then this is not difficult to see using equivariant sheaves (see related comments at the beginning of "tilting exercises" by Beilinson, Bezrukavnikov, Mirkovic). |
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Apr 26 |
asked | Divisibility of all entries in an intersection form |
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Apr 19 |
comment |
Decomposition of C' Kazhdan-Lusztig basis element associated to longest word in S_n I think that this would be very difficult in general, as it depends on choices of reduced expression. Ben Elias has found a nice answer for dihedral groups in terms of representations of sl_2. However you are asking about $S_n$, so these results probably aren't so useful. |
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Mar 23 |
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is this intersection complex a sheaf? Another point of view which might be useful: If $X = X_1 \times X_2$ then $IC(L_1 \boxtimes L_2) = IC(L_1) \boxtimes IC(L_2)$ and so one can reduce to the case of a line. |
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Feb 17 |
answered | Applications for intersection (co)homology and for the Decomposition Theorem for students? |
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Jan 5 |
comment |
small maps, extension of IC sheaves and BM homology I think it is correct that the total spaces of the two resolutions involved are isomorphic, however as you point out the isomorphism does not commute with the projection to $X$. (In the general case I guess it should be true that all small resolution $X' -> X$ have equal motives over $X'$ (point counts of all fibres agree, total cohomology agrees etc.), however this is still a long way away from being isomorphic as varieties.) |
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Jan 4 |
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small maps, extension of IC sheaves and BM homology Hello again! With regards to your question 3, the Atiyah flop (see wikipedia) gives two inequivalent resolutions of the singularity $xw = yz$ in $C^4$. (This singularity occurs in a Schubert variety in the Grassmannian of 2-planes in 4 space.) |
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Jan 3 |
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small maps, extension of IC sheaves and BM homology Hi Dragos, it seems that your definition in the second paragraph is for a semi-small map rather than a small map? |
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Dec 16 |
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Morphisms between Verma modules Good question! I remember talking to Soergel about this a while ago. If memory serves me right he told me that this is no longer true on partial flag varieties, but unfortunately I can't remember where the first counterexample occurs. Also I have often wondered about torsion in the cohomology of these intersections, but I haven't gotten beyond wondering... (some motivation for why one might care is in the section on R-varieties in arxiv.org/abs/1209.3760). |
