Seminar Algebra and Geometry: Jörg Winkelmann (Ruhr-Universität Bochum)

Group actions, entire curves and rational points

Conjecturally abundance of entire curves is closely related to abundance of rational points on projective varieties defined over a number field.

This is discussed in connection with algebraic groups and prinicipal bundles. More precisely, let X be a projective manifold, G an algebraic group and E a G-principal bundle on X, all defined over some number field K. Then E admits a Zariski
dense set of L-rational points for some finite extension field iff X does. This corresponds to the homotopy lifting property whose complex analytic analogue allows to lift entire curves.

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