Abstract :
In this paper we prove that every finite dimensional commutative Hopf Algebra is geometrically reductive. In the case of characteristic zero, this implies that it is the sum of simple subcoalgebras. Then we study the case of characteristic p and relate the geometric reductivity of a Hopf algebra with the corresponding property of its Frobenius kernels. Along the way, we prove some results on finite generation of invariants.
