On the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces

Details On the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces On the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces

2009-06-11

arxiv.org/abs/0906.2056v1

Mathematics

Number Theory

Scientific paper

We study the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces with respect to morphisms of a particular kind. We obtain upper bounds for the arithmetic self-intersection number of the dualizing sheaf on minimal regular models of the modular curves associated with congruence subgroups $\Gamma_0(N)$ with square free level, as well as for the modular curves X(N) and the Fermat curves with prime exponent.

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