Timeline for Interesting "epimorphisms" of $E_\infty$-ring spectra
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 31, 2020 at 20:27 | vote | accept | Maxime Ramzi | ||
| Oct 31, 2020 at 19:46 | answer | added | John Rognes | timeline score: 2 | |
| Aug 26, 2020 at 17:40 | comment | added | Tyler Lawson | The following question discusses how one can have an affine open subscheme Spec(R) of Spec(A) such that R is not a localization. I believe that this should give you an example which is not only connective, but purely algebraic. mathoverflow.net/questions/133470/… | |
| Aug 26, 2020 at 16:29 | comment | added | Maxime Ramzi | @TylerLawson : do you know if there are examples like this where everything stays connective ? (I don't know any spectral algebraic geometry, so I don't really have any intuition about this question) | |
| Aug 25, 2020 at 22:56 | comment | added | Tyler Lawson | The references do discuss how quasi-affines become affine, and in particular Lurie shows that quasicoherent sheaves on a quasi-affine are equivalent to modules over the (derived) global section ring. This gets back at your original motivation because q-c sheaves on an open subscheme of an affine are more easily seen to be a full subcategory of q-c sheaves on the affine itself. | |
| Aug 25, 2020 at 21:56 | comment | added | Maxime Ramzi | @TylerLawson : thanks ! Do the references you give in the beginning of that answer provide a proof of that precise statement or do they dicsuss "this phenomenon" in general ? And I'm guessing spectral algebraic geometry provides other examples of that type ? (Since you seem to say that usual quasi-affines becoming affines is a general phenomenon, and I'm guessing that similar results should hold there) | |
| Aug 25, 2020 at 21:39 | comment | added | Tyler Lawson | The map $\Gamma(\Bbb A^2, \mathcal{O}) \to \Gamma(\Bbb A^2 \setminus 0, \mathcal{O})$, when derived, induces such a map of $E_\infty$ rings. This is discussed a little here: mathoverflow.net/questions/268614/… | |
| Aug 25, 2020 at 13:17 | history | asked | Maxime Ramzi | CC BY-SA 4.0 |