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Apr
14
comment Is Koszulity equivalent to the Lusztig character formula holding?
Basically yes. My understanding is that "positive grading with semi-simple degree 0" is the really hard part (i.e. the bridge the KL polynomials). I expect that in the examples one has once one knows Lusztig style conjectures then Koszulity should hold. (By the numerical criterion for example, as Ben mentions.)
Apr
14
comment Is Koszulity equivalent to the Lusztig character formula holding?
Perhaps the intro of "Modular Koszul duality" arxiv.org/pdf/1209.3760v1.pdf is helpful. In particular the remarks after Theorem 1.2.1
Apr
14
comment Is Koszulity equivalent to the Lusztig character formula holding?
Kazhdan-Lusztig and Lusztig type conjectures are equivalent to a certain graded ring being positively graded and semi-simple in degree zero. Of course this is step 0 towards being Koszul!
Apr
13
comment Chasing a 1950s thesis from the University of Dhaka on block designs
OK! "Refixed" :)
Apr
13
revised Chasing a 1950s thesis from the University of Dhaka on block designs
added 2 characters in body; edited title
Apr
13
awarded  Autobiographer
Apr
13
awarded  Nice Question
Apr
13
comment Chasing a 1950s thesis from the University of Dhaka on block designs
@DimaPasechnik: thanks! fixed...
Apr
13
revised Chasing a 1950s thesis from the University of Dhaka on block designs
deleted 1 character in body; edited title
Apr
12
comment Reference for affine Grassmanian
Dr Evil will you spare me if I give you a reference? I love these notes, and I'm sure it's in there somewhere: arxiv.org/abs/1603.05593
Apr
12
asked Chasing a 1950s thesis from the University of Dhaka on block designs
Apr
6
awarded  Revival
Apr
6
answered The coxeter number condtion in the quantum Lusztig conjecture
Apr
4
comment Is the category of mixed Hodge modules bi-filtered?
It is probably helpful to think about a variation of pure Hodge structure. The associated graded for the Hodge filtration not a pure variation of Hodge structure. (Think about a non-trivial variation of Hodge structure of type (1,1) given by the $H^1$ of a family elliptic curves. One wants to think about this object as being "simple", so it shouldn't break up any further.)
Mar
17
awarded  Nice Answer
Mar
15
comment Push forward of the constant sheaf for a Serre's fibration
I think I was too hasty. Will try to think a bit more...
Mar
14
comment Push forward of the constant sheaf for a Serre's fibration
Yes, this is the proper base change theorem. This is proved for example in "Sheaves on manifolds" by Kashiwara-Schapira. This is also discussed in detail here: front.math.ucdavis.edu/1404.7630 (their interest is more general, but the discussion is useful even in the "classical" case).
Feb
24
comment What are the most misleading alternate definitions in taught mathematics?
Sheaves on Manifolds is by Kashiwara and Schapira.
Feb
23
awarded  Nice Question
Feb
22
answered Non semi-simple monodromy in an algebraic family