Abstract
Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane.
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Ballico, E., Tognoli, A. Algebraic models defined over Q of differential manifolds. Geom Dedicata 42, 155–161 (1992). https://doi.org/10.1007/BF00147546
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DOI: https://doi.org/10.1007/BF00147546