On the p-adic Second Main Theorem

2013/03/17 by Levin, Aaron
#32P05 (Primary) 32H30 #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT) #llJ97 (Secondary)

paper · doi:10.48550/arxiv.1303.4122

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 Pⁿ and D₁,..,D_q are hypersurfaces of degree d, we prove the defect relation ∑_i=1^qδ_f(D_i)≤ n-1+1/d, which is sharp for all positive integers n and d.

Related

• A p-adic Second Main Theorem
• A Non-Archimedean Second Main Theorem for Hypersurfaces in Subgeneral Position
• Entire holomorphic curves into ℙⁿ(ℂ) intersecting n+1 general hypersurfaces
• On non-Archimedean curves omitting few components and their arithmetic analogues
• A refined form of the second main theorem on complete non-positively curved Kähler manifolds