2025/03/24 by Nart, Enric, Novacoski, Josnei
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.18827
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 a previous paper, 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.