F. Oort

We restrict ourselves to two aspects of the field of group schemes, in which the results are fairly complete: commutative algebraic group schemes over an algebraically closed field (of characteristic different from zero), and a duality theory concern­ ing abelian schemes over a locally noetherian prescheme. The prelim­ inaries for these considerations are brought together in chapter I. SERRE described properties of the category of commutative quasi-algebraic groups by introducing pro-algebraic groups. In char8teristic zero the situation is clear.