Timeline for Is there a category-theoretic definition of the arithmetic Grothendieck group
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Sep 24 at 15:04 | comment | added | Z. M | The link to Rössler's paper died, and here is a currently working link: people.maths.ox.ac.uk/rossler/mypage/pdf-files/… | |
| Aug 26, 2011 at 14:04 | comment | added | Damian Rössler | @Ariyan The arithmetic Grothendieck group is devised to approximate the Grothendieck group of a scheme over $\bf Z$, "compactified" at $\infty$; this "compactified" object never appears as such in Arakelov geometry and maybe (probably) doesn't exist. This suggests that there is no natural categorical definition of the arithmetic Grothendieck group. Notice also that since the direct image in $\hat{K}_0$ involves the analytic torsion, which is highly analytic, such a definition would have to include an sort of algebraic interpretation of the latter, which seems to be a tall order. | |
| Oct 27, 2010 at 9:26 | history | edited | Bjørn Kjos-Hanssen |
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| May 30, 2010 at 14:32 | vote | accept | Ariyan Javanpeykar | ||
| Apr 14, 2010 at 16:11 | comment | added | Ariyan Javanpeykar | The "arithmetic curves case" is treated really nicely in Rossler's math.u-psud.fr/~rossler/mypage/pdf-files/rossler-diplom.pdf . If you're still wondering what this secondary Chern form is you should look at pages 16-18. | |
| Apr 12, 2010 at 18:39 | comment | added | Ariyan Javanpeykar | Basically, all of the above is written down really carefully in Faltings's "Lectures on the arithmetic Riemann-Roch theorem". You can find it on google books. Unfortunately, the pages 19-20 are missing from it. | |
| Apr 12, 2010 at 17:35 | answer | added | some guy on the street | timeline score: 2 | |
| Apr 12, 2010 at 17:33 | comment | added | some guy on the street | Could you say a little more about this "secondary Chern form"? I can't find a good reference on-line. | |
| Apr 12, 2010 at 8:31 | history | asked | Ariyan Javanpeykar | CC BY-SA 2.5 |