**Question:** Consider algebraic manyfold assume its number of points is q^n ( [n+1]_q ) does it apply any geometric relation to A^n (P^n)  ? 
In particular is there equivalence in Grothendieck ring of varieties ? Or may be birational equivalence ?

If it is not true in general, may be some additional reasonable requirments on a manyfold will force that to be true ?  

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**Motivation:** one can see that some examples of identities on the level of F_q points enumeration can be lifted to geometric relations:

https://mathoverflow.net/questions/299581/is-there-a-lift-of-the-q-vandermonde-identity-to-some-geometric-motivic-identi

https://mathoverflow.net/questions/299748/can-one-divide-algebraic-manifolds-make-sense-gr2-n-gr2-nm-pn-1-p?noredirect=1&lq=1