Timeline for Field extensions in Grothendieck rings
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 31, 2021 at 22:37 | vote | accept | THC | ||
| Mar 13, 2020 at 16:32 | comment | added | Mikhail Bondarko | Since Shinder's answer is better, I will only say that in the case char(k)=0 one can apply Theorem 4 of Gillet H., Soulé C., Descent, motives and K-theory// J. f. die reine und ang. Math. v. 478, 1996, 127-176, to numerical motives (that coincide with Chow ones for varieties of dimension 0). | |
| Mar 13, 2020 at 11:40 | comment | added | THC | @MikhailBondarko : Yes, very interested ! | |
| Mar 12, 2020 at 20:49 | answer | added | Evgeny Shinder | timeline score: 7 | |
| Mar 12, 2020 at 19:15 | comment | added | Mikhail Bondarko | Actually, if k is of characteristic 0 then my claim is an easy application of the results of Gillet and Soule. Would you like me to turn this into an answer? I can also prove the statement if k is of characteristic $p>0$; yet then I will have to cite my own results.:) | |
| Mar 12, 2020 at 19:00 | comment | added | Mikhail Bondarko | I can try to explain why the equality of classes implies that the (Artin) motives of these fields over k are isomorphic. Unfortunately, it does not follow that the fields itself are isomorphic; thus I doubt that the converse implication is vald. Are you interested? | |
| Mar 12, 2020 at 8:20 | comment | added | YCor | Fine. Anyway if you have in mind arithmetic manifolds [nt.number-theory] or [analytic-number-theory] will probably be more useful. If you have in mind Kähler manifolds, [complex-geometry]. | |
| Mar 12, 2020 at 8:08 | comment | added | THC | @YCor : I indeed understand the tag. And some of the most interesting open cases (related to my question) I know of, arise from / give rise to isospectral manifolds. | |
| Mar 12, 2020 at 1:12 | comment | added | YCor | PS the tag [arithmetic-geometry] would perfectly fit this question in lieu of the wrong one. FYI at this moment, [arithmetic-geometry]: 224 watchers, 1426 questions; [sp.spectral-theory]: 81 watchers, 683 questions. | |
| Mar 12, 2020 at 0:34 | comment | added | YCor | I removed the tag "spectral theory" and you added it again. Have you seen what questions are asked with this tag? Have you seen what are the arxiv papers with this tag? The usage guidance of this tag is Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices. Putting this tag just spams people not interested with this stuff... | |
| Mar 11, 2020 at 18:28 | history | edited | THC |
The tag "spectral theory" is not obvious, but (very) relevant. Especially for (A).
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| Mar 11, 2020 at 18:26 | history | edited | YCor | CC BY-SA 4.0 |
removed irrelevant tag, completed definitions (according to comments)
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| Mar 11, 2020 at 18:16 | comment | added | THC | @Sasha : yes, I consider them as $k$-schemes, and compare the classes in $K_0(V_k)$. (Did I miss something ?) | |
| Mar 11, 2020 at 18:14 | comment | added | Sasha | @THC: What do you mean by the equalities? Do you consider $Spec(K)$ and $Spec(K')$ as $k$-schemes and compare their classes in $K_0(V_k)$? This is quite unclear... | |
| Mar 11, 2020 at 18:07 | comment | added | THC | @YCor : I have no idea what you mean ... | |
| Mar 11, 2020 at 16:58 | comment | added | YCor | You're using the notation $[]$ without defining it, and you're defining $K_0$ without using it. | |
| Mar 11, 2020 at 16:40 | history | asked | THC | CC BY-SA 4.0 |