Timeline for Subtori of restriction of scalars
Current License: CC BY-SA 2.5
5 events
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Dec 3, 2010 at 20:39 | comment | added | Kevin Buzzard | Actually, because you didn't assume $E/F$ Galois the question is actually "what are the $\mathbf{Q}[G]$-submodules of $\mathbf{Q}[G/H]$? (the vector space with basis $G/H$ with $G$ acting on the left). This is still very well-understood. | |
Dec 3, 2010 at 19:49 | comment | added | Kevin Buzzard | In fact, because they're saturated, aren't you just asking for $\mathbf{Q}[G]$-submodules of $\mathbf{Q}[G]$? And this is standard. | |
Dec 3, 2010 at 19:48 | comment | added | Kevin Buzzard | You can use the equivalence of categories between tori and free f.g. abelian groups plus Galois action to turn this in to a purely representation-theoretic question: "if $G$ is a finite group then what are the $G$-stable saturated (i.e. no torsion in cokernel) subgroups of $\mathbf{Z}[G]$". Then an algebraist might be able to help. | |
Dec 3, 2010 at 17:22 | history | edited | Paul Broussous | CC BY-SA 2.5 |
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Dec 3, 2010 at 17:08 | history | asked | Paul Broussous | CC BY-SA 2.5 |