Published online by Cambridge University Press: 01 March 2008
Let be an abelian scheme over a scheme S which is quasi-projective over an affine noetherian scheme and let
be a symmetric, rigidified, relatively ample line bundle on
. We show that there is an isomorphism
of line bundles on S, where d is the rank of the (locally free) sheaf
. We also show that the numbers 24 and 12d are sharp in the following sense: if N>1 is a common divisor of 12 and 24, then there are data as above such that