Timeline for Spectrum of the Grothendieck ring of varieties
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 31, 2022 at 16:15 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed
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| Oct 18, 2009 at 0:50 | comment | added | Theo Johnson-Freyd | Incidentally, another article by Schanuel, namely MR1173024, is more mathematical, and certainly more interesting for this discussion. For example, he computes the Burnside rings for various geometric categories, mostly those whose objects comprise the Boolean ring generated by positive solutions to polynomials/R (resp linear functions) and whose maps are piecewise polynomial (resp affine). He also discusses the case of varieties/C, but remarks that the Burnside ring is too complicated to actually compute (he computes a useful quotient). | |
| Oct 18, 2009 at 0:01 | comment | added | JSE | Cool! So does this actually give a homomorphism from K_0(Var/R) to Z? | |
| Oct 17, 2009 at 19:46 | comment | added | Theo Johnson-Freyd | That's just because you're measuring real Euler characteristic wrong. A better, for certain purposes, Euler characteristic is given by Schanuel in MR0842922 and other articles. For finite cell complexes (like CW complexes, but don't require that each cell have compact closure), the formula is just the alternating sum of the number of cells at each dimension. So e.g. R has one 1-cell and nothing else: Schanuel's euler characteristic is -1 in this case. | |
| Oct 17, 2009 at 9:32 | comment | added | Ilya Nikokoshev | Yes, there are many interesting directions one might explore over different fields! I think it's quite straightforward that Mot is not a domain over C, yes. | |
| Oct 16, 2009 at 15:18 | history | edited | JSE | CC BY-SA 2.5 |
corrected false statement
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| Oct 16, 2009 at 2:08 | history | edited | Ben Webster♦ | CC BY-SA 2.5 |
edited body; added 3 characters in body
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| Oct 16, 2009 at 1:22 | history | answered | JSE | CC BY-SA 2.5 |