THETA GROUPS OVER EXTENSIONS OF ABELIAN VARIETIES BY UNIPOTENT GROUPS

Let 0 -> K-U (i)(->) Y (pi)(->) X -> 0 be a sequence of morphisms of algebraic groups over an algebraically closed field k, where X is an abelian variety, K-U is a unipotent, connected and commutative group scheme, and (X, pi) is a geometric quotient of Y by K-U. If L is an invertible sheaf over X, in this paper we generalize to (L) over bar = pi * L the notion of a theta group associated with an invertible sheaf given by D. Mumford for an abelian variety.