Determinant bundles for abelian schemes

Details Determinant bundles for abelian schemes Determinant bundles for abelian schemes

1997-03-18

arxiv.org/abs/alg-geom/9703021v2

Mathematics

Algebraic Geometry

26 pages, AMSLatex. One proof is shortened, a new linear relation between determinant bundles is proven

Scientific paper

To a symmetric, relatively ample line bundle on an abelian scheme one can associate a linear combination of the determinant bundle and the relative canonical bundle, which is a torsion element in the Picard group of the base. We improve the bound on the order of this element found by Faltings and Chai. In particular, we obtain an optimal bound when the degree of the line bundle d is odd and the set of residue characteristics of the base does not intersect the set of primes p dividing d, such that $p\equiv -1\mod(4)$ and p<2g, where g is the relative dimension of the abelian scheme. Also, we show that in some cases these torsion elements generate the entire torsion subgroup in the Picard group of the corresponding moduli stack.

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