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Apr
6
awarded  Popular Question
Mar
25
comment Useful, non-trivial general theorems about morphisms of schemes
Somoth/étale morphisms can be lifted (Zariski-locally on the source) along closed immersions (EGA IV_4, 18.1.1).
Mar
24
comment Stability of adjunctions of infinity-categories by base change
@YonatanHarpaz: I see now: the assignment $C \mapsto C \otimes_O O'$ is only functorial with respect to left adjoints (as Dylan already pointed out!), so there is no canonical choice for $v'$. Thanks for clearing that up!
Mar
24
asked Stability of adjunctions of infinity-categories by base change
Mar
4
awarded  Enlightened
Mar
4
awarded  Nice Answer
Feb
25
comment Switching left and right adjoints in recollement situations
@domenicofiorenza They must be inverse to each other because they form an adjunction. This is a general category-theoretic fact, of course.
Feb
25
comment Switching left and right adjoints in recollement situations
@domenicofiorenza $\Sigma$ is an equivalence by the definition of triangulated category...
Feb
22
revised Is the hom-simplicial set in the hammock localization a nerve?
edited tags
Feb
17
reviewed Approve Reference Request for Hilbert Schemes
Jan
28
answered Do $RHom(C,D)$ and $DG(C,D)$ have equivalent homotopy categories?
Jan
23
awarded  Good Answer
Jan
22
comment Why do people say DG-algebras behave badly in positive characteristic?
Outside characteristic zero, you have to use $E_\infty$-dg-algebras instead of strictly commutative dg-algebras. See Tyler Lawson's answer here: mathoverflow.net/a/23885/2503. (Oops, Denis beat me to it.)
Jan
9
comment (really) basic intuition for $\mathbb A^1$-homotopy theory
I would recommend taking a look at these notes: dropbox.com/s/6a9jnkqf3f55cs8/…
Jan
1
comment Characterization of closed immersions at the level of perfect complexes
@EldenElmanto, that's an interesting approach (and $f$ being a (homotopy) monomorphism is indeed equivalent to $f^*$ being fully faithful).
Dec
20
awarded  Enlightened
Dec
20
awarded  Nice Answer
Dec
15
answered Motivation and potential applications of spectral algebraic geometry
Dec
14
comment Motivation and potential applications of spectral algebraic geometry
As for your question, I believe that connective DAG (built out of connective E_oo-ring spectra or simplicial commutative rings), is the right generality to deal with questions about algebraic geometry, while nonconnective DAG (= SAG) was really developed with topological applications in mind.
Dec
14
comment Motivation and potential applications of spectral algebraic geometry
The term "derived algebraic geometry" is often used synonymously with what you call "spectral algebraic geometry". The work of Gaitsgory-Lurie, as far as I know, does not use any derived or spectral geometry (though it does use $(\infty,1)$-category theory in an essential way).