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Community Bot
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Let $k$ be a number field and $M$ be a nonzero finite discrete $\mathrm{Gal}(\bar k/k)$-module. Is it true that $H^1(k,M)$ is infinite?

This would complete the answer of Daniel Loughrananswer of Daniel Loughran. There is a comment of nfdc to that answer, but I think that this question deserves an answer rather than just a comment!

Let $k$ be a number field and $M$ be a nonzero finite discrete $\mathrm{Gal}(\bar k/k)$-module. Is it true that $H^1(k,M)$ is infinite?

This would complete the answer of Daniel Loughran. There is a comment of nfdc to that answer, but I think that this question deserves an answer rather than just a comment!

Let $k$ be a number field and $M$ be a nonzero finite discrete $\mathrm{Gal}(\bar k/k)$-module. Is it true that $H^1(k,M)$ is infinite?

This would complete the answer of Daniel Loughran. There is a comment of nfdc to that answer, but I think that this question deserves an answer rather than just a comment!

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Mikhail Borovoi
Mikhail Borovoi
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Infiniteness of the Galois cohomology over a number field with coefficients in a finite Galois module

Let $k$ be a number field and $M$ be a nonzero finite discrete $\mathrm{Gal}(\bar k/k)$-module. Is it true that $H^1(k,M)$ is infinite?

This would complete the answer of Daniel Loughran. There is a comment of nfdc to that answer, but I think that this question deserves an answer rather than just a comment!