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On the $ p$-adic Second Main Theorem


Author: Aaron Levin
Journal: Proc. Amer. Math. Soc. 143 (2015), 633-640
MSC (2010): Primary 32P05; Secondary 32H30, 11J97
Published electronically: October 3, 2014
MathSciNet review: 3283650
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Abstract: 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 $ \mathbb{P}^n$ and $ D_1,\ldots , D_q$ are hypersurfaces of degree $ d$, we prove the defect relation

$\displaystyle \sum _{i=1}^q\delta _f(D_i)\leq n-1+\frac {1}{d},$    

which is sharp for all positive integers $ n$ and $ d$.

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Additional Information

Aaron Levin
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: adlevin@math.msu.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12530-5
Received by editor(s): April 14, 2013
Published electronically: October 3, 2014
Communicated by: Ken Ono
Article copyright: © Copyright 2014 American Mathematical Society