Timeline for What does it mean that $[X]+[Y]=0$ in the Grothendieck ring of varieties?
Current License: CC BY-SA 3.0
8 events
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| Apr 13, 2017 at 16:14 | comment | added | user2520938 | @DanPetersen I figured that much yea. No one here has proven that $[X]=0\Rightarrow X=\emptyset$ "directly". I figured that these approaches that make it seem easy must have some more stuff going on underneath the surface. | |
| Apr 13, 2017 at 16:11 | comment | added | Dan Petersen | A comment: the fact that the functions $N(-)$ and $P(-,t)$ defined on smooth projective varieties give rise to well defined motivic measures is not obvious; if you want to prove it, you should use the Bittner presentation of the Grothendieck ring. | |
| Apr 13, 2017 at 13:28 | history | edited | HYL | CC BY-SA 3.0 |
Add the argument involving the Poincaré polynomial.
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| Apr 13, 2017 at 12:33 | history | edited | HYL | CC BY-SA 3.0 |
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| Apr 13, 2017 at 12:29 | history | edited | HYL | CC BY-SA 3.0 |
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| Apr 13, 2017 at 12:26 | comment | added | Artur Jackson | Nice. Lots of nice proofs. | |
| Apr 13, 2017 at 12:25 | history | edited | HYL | CC BY-SA 3.0 |
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| Apr 13, 2017 at 12:20 | history | answered | HYL | CC BY-SA 3.0 |