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bio website math.jhu.edu/~beardsle
location Baltimore, MD
age 26
visits member for 3 years, 4 months
seen 3 hours ago

Learning.


2d
comment Why Cech cohomology does not compute sheaf cohomology on an open annulus
@DenisNardin aha. good point.
2d
comment Why Cech cohomology does not compute sheaf cohomology on an open annulus
I should add that I have no idea what a Stein manifold is, but topologically at least, the first cohomology of the annulus should be exactly one copy of your coefficients.
2d
comment Why Cech cohomology does not compute sheaf cohomology on an open annulus
I mean, I guess what I'm saying is that my initial guess would be that the first cohomology of the annulus would be one dimensional and that you've produced a generator, but I'm not so good at this stuff.
2d
comment Why Cech cohomology does not compute sheaf cohomology on an open annulus
Are you expecting the Cech cohomology of the annulus to be trivial?
Mar
12
comment Definition of relative Picard functor
@Justin have you worked this out? I'd love to see what you came up with. If not, have you considered thinking about the relative Picard group of a morphism in terms of the first non-abelian cohomology? That produces a pretty good notion of relative Picard group (see Knus and Ojanguran's book for instance).
Mar
11
comment Are n-truncated quasicategories a model for n-categories?
Aaron and I had a talk about this in the homotopy chat room. Apparently my second question is essentially the so-called Baez-Dolan Stabilization Hypothesis, which is proven for (n,1)-categories by Lurie in DAG VI.
Mar
11
comment Are n-truncated quasicategories a model for n-categories?
@AaronMazel-Gee, what's an $E_\infty$-object in an $n$-category for finite $n$?
Mar
9
asked Are n-truncated quasicategories a model for n-categories?
Mar
1
comment Forms of algebraic varieties
More generally, such "forms" of $Y$ are classified by this cohomology group for any morphism which is of effective descent. I think Waterhouse's "An Introduction to Affine Group Schemes" is really helpful.
Feb
23
comment Are submodules of free modules free?
@ACL ah oui, sans doute, desolee. mais je parle seulement l'anglais (as you can probably tell). :-(
Feb
22
comment Are submodules of free modules free?
This has gotten out of control. =P
Feb
19
comment Homotopy limit of a cosimplicial category
What precisely do you mean by "compute"?
Feb
11
comment How is a descent datum the same as a comodule structure?
Hey @Sam for the above equivalence, does one need faithful flatness?
Feb
5
comment origin of spectral sequences in algebraic topology
@RicardoAndrade I would argue that the Kunneth spectral sequence you mention does in fact come from a filtration of the tensor product, if one cellularly approximates one's modules and then essentially looks at all possible products of cells, graded by total "dimension." See, e.g., Sean Tilson's thesis.
Feb
3
comment Are deformations of a scheme some kind of a “derived gerbe” under the cotangent complex?
What's really happening in the usual case of cohomology is that you're looking for maps from $X_0$ to various deloopings of $\mathcal{G}_{X_0/S}$ (a sheaf of abelian groups). Now, however, you want to deloop a sheaf valued in chain complexes, which can be, and is done, and look at morphisms from $X_0$ into that.
Feb
3
comment Are deformations of a scheme some kind of a “derived gerbe” under the cotangent complex?
I'll just say this - at least some of the ideas you're interested in have been approached by homotopy theorists, like Jacob Lurie, and by category theorists. Unfortunately, this seems to be primarily done in the language of infinity categories/infinity topoi (of which the category of chain complexes of sheaves of Abelian groups on some site is an example). However, I'm pretty certain there must be an affirmative answer to your question. One place to start might be ncatlab.org/nlab/show/infinity-gerbe.
Feb
3
comment Are deformations of a scheme some kind of a “derived gerbe” under the cotangent complex?
Hm... maybe you did already.
Feb
3
comment Are deformations of a scheme some kind of a “derived gerbe” under the cotangent complex?
Could you say what it means for a stack to be a gerbe "under a sheaf"? I'm not familiar with that terminology.
Feb
3
accepted Which morphisms of ring spectra are of effective descent for modules?
Feb
3
comment Higher Descent Cohomology
The short answer, for the record, is no. Nobody has done this.