Timeline for What is the meaning of the ideal class group?
Current License: CC BY-SA 4.0
28 events
| when toggle format | what | by | license | comment | |
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| May 1, 2022 at 17:08 | answer | added | Oscar Lanzi | timeline score: 1 | |
| Jan 25, 2022 at 9:46 | audit | First questions | |||
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| Jan 25, 2022 at 7:52 | audit | First questions | |||
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| Jan 24, 2022 at 17:09 | audit | First questions | |||
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| Jan 24, 2022 at 17:03 | audit | First questions | |||
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| Jan 23, 2022 at 19:15 | audit | First questions | |||
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| Jan 21, 2022 at 4:14 | audit | First questions | |||
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| Jan 21, 2022 at 0:41 | audit | First questions | |||
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| Jan 16, 2022 at 15:00 | audit | First questions | |||
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| Jan 10, 2022 at 1:30 | vote | accept | Adithya Chakravarthy | ||
| Jan 8, 2022 at 22:34 | audit | First questions | |||
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| Jan 7, 2022 at 17:03 | audit | First questions | |||
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| Jan 7, 2022 at 12:00 | history | tweeted | twitter.com/StackMath/status/1479422591706320896 | ||
| Jan 6, 2022 at 0:22 | answer | added | Davide Radaelli | timeline score: 2 | |
| Jan 5, 2022 at 18:30 | comment | added | Bill Dubuque | You might also find of interest the papers I cite in this answer which study the relationship between (non)unique factorization and corresponding properties in the set of norms. | |
| Jan 5, 2022 at 12:24 | comment | added | Bill Dubuque | It's not clear why you say the prior threads don't answer you question, because the line of research I describe in this answer certainly does so (I just updated it). Maybe you are seeking simpler arithmetical characterizations of class groups, but I don't believe anything simpler is currently known (except in special cases). | |
| Jan 4, 2022 at 22:47 | audit | First questions | |||
| Jan 5, 2022 at 0:15 | |||||
| Jan 4, 2022 at 9:26 | comment | added | user23365 | @chaad: Why should the class group do that? | |
| Jan 4, 2022 at 7:32 | history | became hot network question | |||
| Jan 4, 2022 at 2:47 | answer | added | Snaw | timeline score: 13 | |
| Jan 4, 2022 at 1:33 | answer | added | WhatsUp | timeline score: 19 | |
| Jan 4, 2022 at 1:18 | answer | added | KCd | timeline score: 31 | |
| Jan 4, 2022 at 1:17 | comment | added | Adithya Chakravarthy | @ThomasAndrews That last sentence is exactly what I'm looking for. How exactly does the class group tell us "in what ways" unique factorization fails? | |
| Jan 4, 2022 at 1:03 | comment | added | Alex Wertheim | (Also, this question is very close in spirit to yours: math.stackexchange.com/questions/538959/… . Might be worth adding to your post, if the information contained therein isn't what you're looking for either.) | |
| Jan 4, 2022 at 0:53 | comment | added | Thomas Andrews | “ This is very unsatisfying though because the exact size of the class group is not used.” That is why people call it a measure of the failure. Obviously, a ring is either a UFD or it is not. The ideal class group doesn’t tell you just whether it fails, but in what way(s). | |
| Jan 4, 2022 at 0:21 | history | edited | Adithya Chakravarthy | CC BY-SA 4.0 |
added 16 characters in body
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| Jan 4, 2022 at 0:06 | comment | added | Alex Wertheim | Very nice question, whose answers I eagerly await. Just one brief comment on your second question: in your example, the exponents of the two groups are different. In particular, in the first case, every element of the class group is $2$-torsion, i.e. $I^{2}$ is principal for every ideal $I$, but the same is not true in the second case. You might be able to view this as some vague measure of how far every ideal is from being principal, at least in this exponent-specific context. Someone more knowledgeable than me could explain this distinction more deeply, I'm sure. | |
| Jan 3, 2022 at 23:32 | history | asked | Adithya Chakravarthy | CC BY-SA 4.0 |