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Jan
11
awarded  Popular Question
Jan
10
comment Gluing affine schemes
Oh man... I feel so misled! Is there some fix? Or should I only trust Grothendieck from now on?
Jan
8
comment Homotopy classes of maps and cohomology classes (Hatcher, AT, Thm 4.57)
You can take, as a model for $K(\mathbb{Z},n)$, the free abelian group on $S^n$ where the basepoint acts as the identity. Then, given an $n$-cocycle $\phi$ you define a map on $X$ by sending the $(n-1)$-skeleton to the basepoint and then sending an $n$-cell $\sigma$ to the sphere by modding out by the boundary, then multiply the result by $\phi(\sigma)$. This gets you to the $n$-skeleton... to extend further you use that $\phi$ was a cocycle.
Jan
7
comment Gluing affine schemes
I.3.3 in Eisenbud-Harris Geometry of Schemes
Jan
6
comment Gluing affine schemes
Not quite: Y isn't necessarily affine so you'll need to make standard opens for local sections not just global sections
Jan
6
comment Gluing affine schemes
EGA II.1.3? You could also define this without gluing: take the underlying topological space to be the set of quasicoherent sheaves of ideals which are prime (which means that sections over each open are prime or the unit ideal.) Now proceed exactly as in the usual case- defining standard opens and the structure sheaf, etc.
Nov
17
comment Model independent proof of colimit formula for left Kan extensions
I think I'm confused by what "model independently" means. The twisted arrow category is model independent, colimits and such are model independent, fibrations and bifibrations are model indepedent... what is the precise thing you take issue with here? For example, in section 5 of the paper you cite, where do we use particular facts about the quasi-category model, for example?
Nov
16
comment Model independent proof of colimit formula for left Kan extensions
The twisted arrow category is model independent and the formula you're looking for is the limit over the twisted arrow category, right?
Nov
11
comment why don't (can't?) we sheafify the structure presheaf of an adic space
Presumably you can sheafify but you'll get the wrong global sections.
Oct
2
comment Is every abelian group a colimit of copies of Z?
@QiaochuYuan A fun fact recently learned by me and long known to others: The answer to the question is yes if we replace $\mathbb{Z}$ by $\mathbb{Z}\oplus \mathbb{Z}$. :)
Sep
26
comment very basic question on p-typical group law and MU and BP
For the latter question, you're probably just tensoring $\xi$ with $MU_*(X)$. After all, $MU_{(p)}{_*}$ is flat over $MU_*$.
Sep
14
comment Is there an octonionic analog of the K3 surface, with implications for stable homotopy groups of spheres?
Can you do a kummer-esque construction to the 8-torus and get anything nice?
Sep
1
comment About the relation between the categories $\text{Sch}$, $\text{LRS}$ and $\text{RS}$
@MarcHoyois: whoops! I've added your amendments and made this community wiki so anyone else can correct as they see fit.
Sep
1
revised About the relation between the categories $\text{Sch}$, $\text{LRS}$ and $\text{RS}$
added 368 characters in body
Aug
31
answered About the relation between the categories $\text{Sch}$, $\text{LRS}$ and $\text{RS}$
Aug
4
comment cohomology ring of cross-section space of one-point compactification of tangent bundle
I think your best bet is computing this using nonabelian Poincaré duality (at least if you're willing to stick with compact manifolds or compactly supported sections). A good reference is arxiv.org/pdf/1206.5522v4.pdf
Aug
3
comment Is a pullback along a Dold fibration a homotopy pullback?
The link doesn't seem to work on the app (for me), but here's the paper: math.uiuc.edu/~rezk/rezk-sharp-maps.pdf
Aug
3
answered Is a pullback along a Dold fibration a homotopy pullback?
Aug
1
answered Reference for (co)limit-preserving functor $X\mapsto R^X$
Jul
28
awarded  Nice Answer