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The support of a finite type module on an algebraic space
added 392 characters in body |
Jun
15 |
comment |
Is there a scheme corresponding to the unit interval?
@Qfwfq: what is a good reference to learn about motivic spheres? @martin: what I don't get about the analogy you are searching is that the first two rows of your table distinguish between real and complex (then "unified" as a scheme), but the third row is just the interval. Seems like one should first understand what is a "complex interval"... |
Jun
15 |
comment |
Is there a scheme corresponding to the unit interval?
Just a comment. The first two rows of your table are quite literal in real algebraic geometry. As for gluing things: if you are dealing with complex geometry, then "correct" gluing of two copies of the "complex interval" you are pursuing strike me as trying to do $\pi_2" rather than $\pi_1$. |
Jun
14 |
comment |
The support of a finite type module on an algebraic space
The coherator is the maximal quasi-coherent sheaf contained in the given sheaf. It might be a substitute for End when the sheaf is only of finite type, but I agree that it doesn't look like it would give you the right support. I thought to ask as you might have known. |
Jun
14 |
comment |
The support of a finite type module on an algebraic space
I think I understand how you'd prove it, I was just surprised not to find in the stacks project. But then again it's not even in the schemes section, so it must have been exactly because of the reason you mentioned: the sheaf is not finitely presented. |
Jun
13 |
comment |
The support of a finite type module on an algebraic space
"And if "yes" then please explain why you can't apply the same argument to answer your question for algebraic spaces." - I think you forgot to write wink wink at the end :). but maybe I can ask a real question: when $F$ is only of finite type, can one not use the coherator of the sheaf hom to get a quasi-coherent sheaf? would that do the trick? |
Jun
13 |
asked | The support of a finite type module on an algebraic space |
May
30 |
comment |
homotopy pullback/pushout
if you accept the fact that the category of spectra is stable, then it follows from the axioms of being stable (how tautological was this comment?) |
May
15 |
comment |
Rigidification and good moduli space (morphism) in the sense of Alper
won't in general the rigidification morphism have higher pushforwards? (so that $\phi_*$ fails to be exact) I guess in characteristic zero this won't happen if you're killing off a finite group. |
May
10 |
answered | Semicontinuity for complexes |
Apr
25 |
comment |
Homotopy-theoretic measure of operations on sheaves failing to be sheaves
side remark: when U is affine in X, $(F \otimes G)(U) = F(U) \otimes G(U)$ (at least when $F$ and $G$ are quasi-coherent). I guess abstractly this is just stating the existence of a basis for the topology of $X$ which plays well with the given colimit construction. (I repeat: side remark) |
Apr
23 |
comment |
Cech Cohomology of Sections of Holomorphic Bundle over Contractible Space
are there examples of contractible but non-affine algebraic varieties? (or contractible but non-Stein analytic spaces?) |