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On the p-adic Second Main Theorem

We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving an improvement to the non-archimedean Second Main Theorems of Ru and An in the case where all the hypersurfaces have degree greater than one and all intersections are transverse. In particular, under a transversality assumption, if f is a nonconstant non-archimedean analytic map to P^n and D_1,..,D_q are hypersurfaces of degree d, we prove the defect relation \sum_{i=1}^qδ_f(D_i)\leq n-1+1/d, which is sharp for all positive integers n and d.

preprint2013arXivOpen access
Aaron Levin
math.CVmath.NT
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Aaron Levin

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