Semi-stable fibrations of generic p-rank 0 |
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Authors: | Junmyeong Jang |
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Institution: | 1. School of Mathematics, Korea Institute for Advanced Study, Kias Hoegiro 87, Dongdaemun-gu, Seoul, 130-722, South Korea
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Abstract: | 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 nonclosed point in the moduli space over a number field. |
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