Timeline for Base change of cohomology when the cohomology is a torsion
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2021 at 13:43 | comment | added | Pickle Liobe | @abx, Well, you may put some suitable conditions on $\mathscr F$, like $\mathscr F$ is supported on $X_k$. | |
| Dec 3, 2021 at 13:34 | comment | added | Pickle Liobe | @PiotrAchinger, That's very true. I have edited the problem. | |
| Dec 3, 2021 at 13:30 | history | edited | Pickle Liobe | CC BY-SA 4.0 |
added 228 characters in body
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| Dec 3, 2021 at 13:06 | history | edited | Pickle Liobe | CC BY-SA 4.0 |
Correct the question description
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| Dec 3, 2021 at 8:58 | comment | added | Piotr Achinger | Since $H^i(X, \mathcal{F})$ is only annihilated by some power of $\mathfrak{m}$, it does not have to be a $k$-vector space. | |
| Dec 3, 2021 at 8:25 | comment | added | abx | Actually your $\mathscr{I}$ is the pull back of $m=(\pi )$, where $\pi $ is a unifomizing parameter for $R$. Thus the left hand map on your exact sequence is just $\ \times \pi : H^i(X,\mathscr{F})\rightarrow H^i(X,\mathscr{F})$. But I don't think you can say anything a priori on its kernel and cokernel. | |
| Dec 3, 2021 at 7:17 | history | edited | Pickle Liobe | CC BY-SA 4.0 |
added 46 characters in body
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| Dec 3, 2021 at 7:00 | history | asked | Pickle Liobe | CC BY-SA 4.0 |