A p-adic Second Main Theorem

2024/05/23 by Dinh Tuan Huynh, Huynh, Dinh Tuan
Mathematics · #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2405.14197

Abstract

Let K be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value | |. We establish a Second Main Theorem type estimate for analytic map f\colon K→ℙⁿ(K) and a family of n hypersurfaces in ℙⁿ(K) intersecting transversally and not all being hyperplanes. This implements the previous work of Levin where the case of all hypersurfaces having degree greater than one was studied.

Related

• On the p-adic Second Main Theorem
• A Non-Archimedean Second Main Theorem for Hypersurfaces in Subgeneral Position
• Hypersurfaces passing through the Galois orbit of a point
• Effective Bertini theorems and zeros of p-adic forms of degrees 7 and 11
• Degrees of closed points on hypersurfaces