Skip to main content
Jacob Lurie's user avatar
Jacob Lurie's user avatar
Jacob Lurie's user avatar
Jacob Lurie
  • Member for 14 years, 5 months
  • Last seen more than 3 years ago
Loading…
awarded
awarded
Loading…
comment
Cochains on Eilenberg-MacLane Spaces
That's the strategy I had in mind. When n=0 you can prove it using deformation theory, so let's try induction on n. Let R(n) be the cofiber and let R'(n) be the cochains on K(Z/pZ,n). Then doing a bar construction on R(n) produces R(n-1), and similarly for R'(n). So the I.H. tells you that the map R(n) -> R'(n) is an equivalence after applying the bar construction. If you knew that R(n) had no positive homotopy and that pi_0 R(n) = k (statements which are obvious for R'(n)), then the bar construction doesn't lose any information and you are done. But a priori R(n) is a big mess.
comment
Cochains on Eilenberg-MacLane Spaces
He also doesn't prove this theorem. Unless I misunderstand, he works in the setting of cosimplicial algebras (where the analogous statement is easy) and uses it to prove variants of Mandell's results.
awarded
asked
Loading…
awarded
comment
Fibered/cofibered higher categories, relative model structures, slicing, and (∞,2)-category theory
If S is a point, then the Cartesian and coCartesian model structures coincide, so induce the same model structure after slicing at X. So the claim can't be true in general, since the Cartesian and coCartesian model structures on marked simplicial sets over X are generally different (they agree when X is a Kan complex). All of these model categories are closely related to the Joyal structure on simplicial sets, which is not right proper. It's generally a bad idea to slice them over non-fibrant objects.
Loading…
comment
Is there a higher homotopical spinor theory?
Should be easy enough to make it central: form the fiber product in simplicial groups, where you can model K(Z/2, m+1) and its path space by simplicial abelian groups. More generally, I believe that simplicial objects in "groups with a central extension" is a model for the homotopy theory of triples (X,Y,f) where f is a pointed connected space, Y is a 1-connected HZ-module spectrum, and f is a map from X to the zeroth space of Y.
comment
Tensor variant of Mitchell's embedding theorem
F(A) = Hom(R, F(A)) = Hom( F(1), F(A) ) = Hom(1, A) if F is fully faithful.
answered
Loading…
comment
Torsors for finite group schemes
I don't know how to answer my question even in that case. Of course, when G is given as the kernel of Frobenius on a smooth group scheme, I can describe G-torsors in terms of the smooth group scheme, as mentioned in the answer below. But that's cheating: I want a description in terms of the Lie algebra. If it helps, it may be sufficient for my application to treat the "toy case" at the other extreme, where g is a free restricted Lie algebra (so G is not a finite group scheme, and some care should be taken with the meaning of "torsor", but I believe the question is still sensible).
comment
Torsors for finite group schemes
So I guess in these terms what I'd like is a more explicit description of the quotient U(g)^x/G. For example, is there some naturally occuring affine space on which U(g)^x acts, where one of the stabilizers is G?
awarded
awarded
revised
Loading…
asked
Loading…