Timeline for An omission in K. Conrad's notes on the conductor ideal
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 18, 2022 at 3:24 | comment | added | KConrad | The "footnote 4" in my previous comment should be "footnote 5". | |
| Apr 16, 2022 at 23:19 | comment | added | KConrad | I updated the file using Will's argument below, so now there is no longer an omission. After adding an example at the start of Section 5, the labels Lemma 5.1 and Theorem 5.2 have turned into Lemma 5.2 and Theorem 5.3 (and the goal of the lemma has been changed). The claim that you wanted is now the first part of Theorem 5.3 and it holds in an arbitrary one-dimensional Noetherian domain, not just in an order in a number field (see footnote 4). | |
| Apr 16, 2022 at 19:43 | comment | added | LSpice | You said "I could prove why this should also occur …", but the question strongly suggested you meant that you could not prove it. I edited accordingly. I hope that this was correct. | |
| Apr 16, 2022 at 19:43 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading; missing 'not' (hopefully correctly)
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| Apr 16, 2022 at 16:57 | history | became hot network question | |||
| Apr 16, 2022 at 16:36 | comment | added | Hair80 | Thank you very much for your very useful answer, this solves the problem I was having | |
| Apr 16, 2022 at 14:35 | answer | added | Will Sawin | timeline score: 17 | |
| Apr 16, 2022 at 6:10 | comment | added | KConrad | Oops! I did not intend to post the file with that incomplete argument. A proof that would be overkill is to identify the ideal class group (Picard group) of the order with a generalized ideal class group and thus Galois group of a finite abelian extension (Theorems 3.8, 3.11, and 4.2 in arxiv.org/abs/1405.5776), so each ideal class should be represented by infinitely many prime ideals. That gives ideals relatively prime to the conductor. I wanted to find a much simpler argument, but I then forgot about it. | |
| Apr 16, 2022 at 4:31 | history | asked | Hair80 | CC BY-SA 4.0 |