Timeline for Can one define a degree of a period?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 3, 2021 at 7:50 | vote | accept | gmvh | ||
| Feb 11, 2021 at 15:37 | comment | added | Sylvain JULIEN | I was indeed a bit doubtful of the relevance of my answer but it might be a first step towards further investigations, and as such I thought it might be somewhat useful to you (and maybe other people as well). | |
| Feb 11, 2021 at 15:12 | comment | added | gmvh | This is indeed more or less answers my question: one can define a degree in terms of the dimension of the region of integration, but this degree is indeed not terribly satisfying, and it doesn't look like the physicists' notion of degree at all (it appears to equal two for all of the periods commonly occurring from Feynman integrals, no matter the loop order). | |
| Feb 11, 2021 at 0:57 | comment | added | Will Sawin | @MattF. IMO one should either (1) assume Grothendieck's period conjecture or (2) define a "period" not as a number but as an integral representing a number, and only allow "algebraic" manipulations, so that each period defines a motive, and we have a reasonable theory. | |
| Feb 10, 2021 at 11:43 | comment | added | user44143 | The paper presents it as a problem to give a concrete period whose degree is $\ge 3$ -- it would be more satisfying to have a notion of degree with more interesting examples. | |
| Feb 10, 2021 at 11:41 | history | edited | user44143 | CC BY-SA 4.0 |
added author and title
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| Feb 10, 2021 at 11:08 | history | answered | Sylvain JULIEN | CC BY-SA 4.0 |