Timeline for Number Rings and (Galois) Descent
Current License: CC BY-SA 4.0
13 events
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| Feb 1, 2019 at 13:42 | history | edited | user30211 | CC BY-SA 4.0 |
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| Feb 1, 2019 at 1:48 | comment | added | F Zaldivar | You are right. I think I can see that that the étale condition gives covering data, but I don't see how to define the cocycle condition to get descent data in a non faithfully flat situation. | |
| Feb 1, 2019 at 1:44 | comment | added | user30211 | I thought about this for a while, but I think $\mathbb{Q} / \mathbb{Z}$ is not faithfully flat, which can be seen from the fact that $\mathbb{Z} / n \mathbb{Z}$ collapses. Something close may be the case though. I will look into the reference you provided, thanks very much. | |
| Feb 1, 2019 at 1:09 | comment | added | F Zaldivar | I think all these is in Waterhouse "Affine Group Schemes" (Springer) and it seems to me that the descent data that generalizes Galois descent in you case is faithfully flat descent. | |
| Feb 1, 2019 at 1:04 | vote | accept | CommunityBot | moved from User.Id=30211 by developer User.Id=481663 | |
| Feb 1, 2019 at 0:23 | answer | added | Alec Rhea | timeline score: 2 | |
| Feb 1, 2019 at 0:10 | history | edited | user30211 | CC BY-SA 4.0 |
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| Feb 1, 2019 at 0:04 | comment | added | user30211 | Sorry, you're right. I forgot those have the right rank. | |
| Jan 31, 2019 at 23:59 | comment | added | Alison Miller | "the number rings O_K are precisely the finite Z-algebras such that O_K⊗Z Q_sep splits into the product of rank_Z(O_K) many Q_sep's. " I don't think this is right: the property you've stated also holds for any order in a number field (or more generally any order in an etale Q-algebra) since it only depends on O_K ⊗Z Q. | |
| Jan 31, 2019 at 23:33 | history | edited | user30211 | CC BY-SA 4.0 |
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| Jan 31, 2019 at 21:36 | history | edited | user30211 | CC BY-SA 4.0 |
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| Jan 31, 2019 at 20:11 | history | edited | user30211 | CC BY-SA 4.0 |
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| Jan 31, 2019 at 19:46 | history | asked | user30211 | CC BY-SA 4.0 |