Timeline for How small can the support of a nontrivial $\mathbb F_p$-cocycle on $C_p$ be?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 5, 2021 at 16:00 | answer | added | Will Sawin | timeline score: 8 | |
| Aug 5, 2021 at 15:28 | comment | added | Tim Campion | @WillSawin That's fantastic! I'd be interested to hear about the details -- I don't know what a property testing argument is. | |
| Aug 5, 2021 at 13:21 | comment | added | Will Sawin | A better cocycle in the $n=2$ case is attained by lifting each residue class mod $p$ to the corresponding element of $-(p-1)/2, - (p-3)/2, \dots, -1, 0, 1, 2, \dots, (p-3)/2, (p-1)/2$, which gives a cocycle with $ (p^2-1)/4$ nonvanishing entries. I can prove a lower bound of $cp^2$ for some $c>0$ (maybe about $1/8$) when $n=2$ by using a property testing argument, but I don't know how to generalize to higher $n$. | |
| Aug 4, 2021 at 23:00 | comment | added | Tim Campion | np! I appreciate your work! | |
| Aug 4, 2021 at 23:00 | comment | added | LSpice |
Sorry about the unwelcome \mathit. There is someone who asked me not to introduce \operatorname into their posts because they don't like its appearance, and I thought it was you, but I must have got mixed up.
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| Aug 4, 2021 at 22:43 | comment | added | Will Sawin | Using the explicit formula for cup product in group cohomology (mathoverflow.net/a/688/18060), applied to the carrying cocycle, you can get an upper bound on the lower bound of $(p (p-1)/2)^{n/2}$. | |
| Aug 4, 2021 at 22:26 | history | edited | Tim Campion | CC BY-SA 4.0 |
clarifying. Also, who disprefers "operatorname" ?
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| Aug 4, 2021 at 22:23 | history | edited | LSpice | CC BY-SA 4.0 |
`\mathit` (since `\operatorname` is dispreferred)
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| Aug 4, 2021 at 22:22 | comment | added | Tim Campion | @LSpice Yes, that's what I mean. | |
| Aug 4, 2021 at 22:21 | comment | added | Tim Campion | I've included the "additive combinatorics" tag because I think that "near homomorphisms" might be studied in that field, but it's possible this is a mis-tag. | |
| Aug 4, 2021 at 22:21 | comment | added | LSpice | What is $C_p$? The cyclic group with $p$ elements? | |
| Aug 4, 2021 at 22:20 | history | asked | Tim Campion | CC BY-SA 4.0 |