On Peterzil-Steinhorn subgroups

Definable compactness and definable subgroups of o-minimal groups" Y. Peterzil and
C. Steinhorn showed that to  any  unbounded curve in a group definable in an o-minimal
structure one can associate a definable one-dimentional subgroup.
Roughly, it is a subgroup that is  "tangent at infinity" to the curve.  In this talk we show
that the same can be done for algebraic groups over arbitrary algebraically closed field.