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Apr 22 at 21:08 comment added Boris @Evgeny Shinder Thank you very much for your kind guidance and help.
Apr 21 at 20:40 comment added Evgeny Shinder If $X$ is a projective toric variety then $A_0(X) = \mathbb{Z}$ (this is true because it's resolution is rationally connected), and then the localization exact sequence implies that for any nontrivial open subset $A_0(U) = 0$.
Apr 13 at 16:13 history asked Boris CC BY-SA 4.0