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Dec
23
comment Fiber functors to derived categories
Is it really true that $G$ linearly reductive implies $\delta=0$? For example, consider a cts homomorphism $\Gamma\rightarrow G(k)$ where $\Gamma$ is a procyclic group ($k$ could be discrete or have an interesting topology). Then the functor $V\mapsto V^\Gamma$ may not be exact, but the group cohomology $H^i(\Gamma,V)$ is likely computed by the complex $V\rightarrow V$, where the map is $\gamma-1$ for a topological generator $\gamma$ of $\Gamma$. If $V\mapsto V^\Gamma$ is exact, it looks to me like I get 2 $G$-torsors (one for $H^0$, one for $H^1$), but if not, I don't think $\delta=0$.
Sep
30
comment Are D_dR and D_st “potentially comparable”?
Great, thanks!
Jul
2
comment Some help in digesting a paragraph in the introduction of Deligne/Rapoport's “Les Schemas de Modules de Courbes Elliptique”
Yes, we're thinking of $(\mathbf{Z}/n\mathbf{Z})^2$ as a group scheme. Over any base scheme $S$, the scheme structure on $(\mathbf{Z}/n\mathbf{Z})_S^2$ is just $n^2$ disjoint copies of $S$.
Dec
25
comment Deformation of ordinary p-divisible groups via Grothendieck-Messing
I think you're implicitly asserting that the map $\omega_{G^m}\rightarrow D(G_0)(W(k))$ coming from $G'$ is the same as the composition $\omega_{G^m}\rightarrow \omega_G\rightarrow D(G_0)(W(k))$.
Dec
24
comment Shape of snowflakes
It's not the same as assuming no molecules attach at the same time, because in your random model you're effectively adjusting the probability of attachment based on the size of the snowflake. If anything, you want to adjust the probabilities based on the geometry --- I would guess that available vertices deep "inside" the snowflake would have lower probabilities of attachment.
Dec
24
comment Shape of snowflakes
I don't like your random model: it seems much more reasonable to fix a probability p and at time t, attach a new hexagon at every available lattice point with probability p. Assuming a fair amount of water in the air, water crystallizing at one vertex should be independent of water crystallizing at other vertices (to a first approximation).
May
8
comment What's the difference between a real manifold and a smooth variety?
Don't these all illustrate the differences between real and complex manifolds, rather than between real manifolds and smooth complex varieties?
Mar
21
comment Chinese Remainder Theorem for rings: why not for modules?
Tensor the map $R/(I_1...I_n)\rightarrow R/I_1\times...\times R_I_n$ over $R$ with $A$.
Feb
15
comment visualizing what's going on in based homotopy theory, et al.
For c), have you looked at chapter 4 of Hatcher's book? Everything there is very geometric.
Dec
4
comment Why is Riemann-Roch an Index Problem?
A lot is brushed under the rug, like carrying out all of these steps on more than a formal level. Also, things like metrics on line bundles are hidden in the definition of the adjoint and the defintion of c_1.
Nov
29
comment Irreducible polynomial over number field with roots in every completion?
That's interesting, do you know where the argument breaks down if K/Q is infinite?
Nov
12
comment Do quotients of representable sheaves represent quotients?
Ah, right - thanks very much.
Nov
12
comment Do quotients of representable sheaves represent quotients?
Yes, sorry. I fixed it.
Nov
8
comment Can we count isogeny classes of abelian varieties?
I'll take a look at those articles, thanks.
Nov
8
comment Can we count isogeny classes of abelian varieties?
Thanks! I'm certainly also interested in the story over $\overline{F}_q$.
Oct
25
comment Best Algebraic Geometry text book? (other than Hartshorne)
He's not posting them online yet; he's been handing out chunks of notes on various topics, but he wants to edit them more before posting.