Geodesic
The group $F^2K(X)$ as a birational invariant of a surface
Matematičeskie zametki, Tome 11 (1972) no. 1, pp. 15-20.

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The birational invariance is proved of the group $F^2K(X)$, where $X$ is a smooth projective surface over a field. 
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     author = {L. R. Gorodetskii},
     title = {The group $F^2K(X)$ as a birational invariant of a surface},
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L. R. Gorodetskii. The group $F^2K(X)$ as a birational invariant of a surface. Matematičeskie zametki, Tome 11 (1972) no. 1, pp. 15-20. http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a1/