Timeline for Cohomology and base change without Noetherian assumption
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| May 7, 2021 at 7:25 | history | edited | Fabian Ruoff | CC BY-SA 4.0 |
added 433 characters in body
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| May 7, 2021 at 7:21 | vote | accept | Fabian Ruoff | ||
| May 5, 2021 at 15:26 | comment | added | Z. M | I would like to point out that it is possible to drop the properness and replace the higher direct image $Rf_*$ by the "pushforward with compact support" $f_!$, which is described in Lectures on Condensed Mathematcs Lecture 11. For sake of simplicity, he described the case of finite type over $\mathbb Z$, but it could be generalized by taking the colimit over finitely generated algebras, see Lectures on Analytic Geometry Prop 13.16. | |
| May 5, 2021 at 15:05 | history | became hot network question | |||
| May 5, 2021 at 12:32 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| May 5, 2021 at 11:55 | answer | added | Leo Alonso | timeline score: 4 | |
| May 5, 2021 at 7:45 | comment | added | Fabian Ruoff | @MatthieuRomagny My mistake, maybe I was not quite clear. I am only looking for a generalization to non-Noetherian schemes (or more precisely a reference). But I thought that it could be included in some result about stacks that I do not understand. | |
| May 5, 2021 at 7:40 | comment | added | Matthieu Romagny | Right -- the point is, you seemed to require a generalization of the "historical" base change theorem in two directions (remove noetherian assumptions ; pass from schemes to stacks) and I was pointing out that for the stack direction, it's in the literature. | |
| May 5, 2021 at 7:30 | comment | added | Fabian Ruoff | @OlivierBenoist They seem to use the same argument as indicated by Vakil. Thank you for the reference, I did not know this one. | |
| May 5, 2021 at 7:28 | comment | added | Fabian Ruoff | @MatthieuRomagny As far as I can tell he only seems to proof a similar theorem to base change (theorem A) using a Noetherian condition. | |
| May 5, 2021 at 7:19 | comment | added | Olivier Benoist | How to reduce to the Noetherian case is detailed in [FGA explained, Proposition 4.37], but the statement there may not be as general as you need. | |
| May 5, 2021 at 7:12 | comment | added | Matthieu Romagny | Is Hall, Jack, Cohomology and base change for algebraic stacks, Math. Z. 278 (2014) useful to you ? | |
| May 5, 2021 at 7:05 | history | asked | Fabian Ruoff | CC BY-SA 4.0 |