Depth of Artin-Schreier defect towers
Abstract
The depth of a simple algebraic extension ( L / K , v ) of valued fields is the minimal length of the Mac Lane-Vaquié chains of the valuations on K [ x ] determined by the choice of different generators of the extension. In [12] , we characterized the defectless unibranched extensions of depth one. In this paper, we analyze this problem for towers of Artin-Schreier defect extensions. Under certain conditions on ( K , v ) , we prove that the towers obtained as the compositum of linearly disjoint defect Artin-Schreier extensions of K have depth one. We conjecture that these are the only depth one Artin-Schreier defect towers and we present some examples supporting this conjecture.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Rings
Modules
and Algebras
Advanced Algebra and Geometry
Publication details
- Journal / source
- Journal of Pure and Applied Algebra
- Volume
- 230
- Issue
- 2
- Pages
- 108184–108184
- Publication date
- 27 January 2026
- Language
- EN