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Stabilo
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
@Joël The previous assumption « dim Krull=1 » would have prevent your counter-example to happen I presume, but you are right that I meant finitely generated as an $R$-algebra. This has been edited. Sorry for being confused, I am at the mean time trying to find the suitable condition on $A$ so that the answer to my question is « yes »...
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
@მამუკაჯიბლაძე Thank you, my question was more than confusing without the condition that $A$ is an $R$-algebra. Hope this is fine now.
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
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Sheaf cohomology on the formal completion of $\mathbb{P}^1_k$ at its north pole
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Sheaf cohomology on the formal completion of $\mathbb{P}^1_k$ at its north pole
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Sheaf cohomology on the formal completion of $\mathbb{P}^1_k$ at its north pole
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Sheaf cohomology on the formal completion of $\mathbb{P}^1_k$ at its north pole
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Sheaf cohomology on the formal completion of $\mathbb{P}^1_k$ at its north pole
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What are the consequences of the finite generation of $\operatorname{Ext}^1_{\mathcal{O}_F}(\mathbb{1},M)$?
If you permit a small addendum to my question: do we expect finite generation of $\operatorname{Ext}^1_{\mathcal{O}_F}(\mathbb{1},M)$ when $M$ has positive weights? It seems to me that Beilinson's conjectures only deal with motives having negative weights...
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Sheaf cohomology on the formal completion of $\mathbb{P}^1_k$ at its north pole
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What are the consequences of the finite generation of $\operatorname{Ext}^1_{\mathcal{O}_F}(\mathbb{1},M)$?
Merci beaucoup François pour ta superbe réponse.
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