Ein Kontinuitätssatz für k-holomorphe Mengen

Abstract

Let k denote a non-trivial non-archimedean complete valuated field and X an irreducible k-affinoid space. We discuss the Hartog's domain H^*:=(X×∂Eⁿ)∪ (U×Eⁿ) where ø≠U⊂X is an affinoid subdomain, Eⁿ is the n-dimensional unit-polydisc over k and ∂Eⁿ is the ringdomain of all z==(z₁,...,z_n)∈Eⁿ with some coordinate |z_i|=1. The main result is the non-archimedean version of Rothstein's extensiontheorem for analytic subvarieties: Every k-holomorphic subvariety A⊂H^* whose every branch has dimension ≥(dim X + 1) can be extended to a k-holomorphic subvariety Ā⊂X×Eⁿ such that every branch of Ā has dimension ⩾(dim X + l).