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The support of a finite type module on an algebraic space
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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 quasicoherent 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 quasicoherent 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 
Homotopytheoretic 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 quasicoherent). 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 nonaffine algebraic varieties? (or contractible but nonStein analytic spaces?) 
Mar 30 
accepted  Applications of topological chiral homology and factorization algebras (aka higher Hochschild cohomology) 