Timeline for Categorification request
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 17, 2011 at 11:46 | comment | added | Martin Brandenburg | Yes. Can't we just conclude that the purpose of Grothendieck constructions is this kind of formal "calculation"? | |
| Feb 17, 2011 at 11:42 | comment | added | Dan Petersen | This type of decomposition should work also "motivically", whatever that is supposed to mean. So the equation also makes sense in the Grothendieck ring of varieties, in the Grothendieck ring of Hodge structures, in the Grothendieck ring of $\ell$-adic Galois representations, etc, when q is the class of the affine line. Note also that $q^{n+1} -1$ is the class of $\mathbf{A}^{n+1}\setminus \{0\}$ and that $q-1$ is the class of $\mathbf{G}_m$, so the equation really expresses that $\mathbf{P}^n$ is the set of lines through a point in an affine space one dimension higher. | |
| Feb 17, 2011 at 11:35 | history | answered | Martin Brandenburg | CC BY-SA 2.5 |