Timeline for Motivic characterization of affine spaces
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 17, 2010 at 14:20 | vote | accept | Alexander Braverman | ||
| Nov 17, 2010 at 14:20 | vote | accept | Alexander Braverman | ||
| Nov 17, 2010 at 14:20 | |||||
| Oct 30, 2010 at 17:02 | history | edited | Torsten Ekedahl | CC BY-SA 2.5 |
added 35 characters in body
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| Oct 30, 2010 at 7:34 | history | edited | Torsten Ekedahl | CC BY-SA 2.5 |
Added one more elaboration
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| Oct 29, 2010 at 11:51 | comment | added | Alexander Braverman | Thank you. My question is now kind of informal: what kind of conditions can one put on a variety so that the answer will be positive? The point is that the varieties I have in mind are very specific and I can probably prove many things about them if I only knew what to prove... | |
| Oct 18, 2010 at 20:50 | comment | added | Qing Liu | By the definition of $K_0$, the class of $X$ only sees the "piece-wise geometry" of $X$: if $X$ and $Y$ are two varieties such that they can be stratified into locally closed subsets $X_1,...,X_n$ and $Y_1,..., Y_n$ with $X_i$ isomorphic to $Y_i$, then $[X]=[Y]$. The converse is a question of Larsen and Luntz. It is true over $\mathbb C$ if $X$ contains only finitely many rational curves (see Q.L & J. Sebag: {\it The Grothendieck ring of varieties and piecewise isomorphisms}, Math. Z., {\bf 265} (2010), 321-342, Theorem 5). But this is orthogonal to your situation. | |
| Oct 17, 2010 at 15:12 | history | edited | Torsten Ekedahl | CC BY-SA 2.5 |
Added further discussion on smooth quadrics
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| Oct 17, 2010 at 14:29 | comment | added | Alexander Braverman | Thank you! Do you know if there is a way to put stronger conditions on $X$, so that the answer will be "yes"? | |
| Oct 17, 2010 at 14:21 | history | answered | Torsten Ekedahl | CC BY-SA 2.5 |