Semi-stable fibration of generic p-rank 0

Details Semi-stable fibration of generic p-rank 0 Semi-stable fibration of generic p-rank 0

2008-05-26

arxiv.org/abs/0805.3997v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

In this paper, we proved that, for a semi-stable fibration of a proper smooth surface to a proper smooth curve over a filed of positive characteristic, if the p-rank of the generic fiber is 0, then the base change of the fibration by a sufficiently many iterative Frobenius morphism of the base curve violates the semi-positivity theorem. As an application, we suggest a statement on a distribution of p-ranks of reductions for a certain non-closed point in the moduli space over a number field.

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