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arXiv · 2503.18827

Depth of Artin-Schreier defect towers

Enric Nart·Josnei Novacoski
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Abstract

The depth of a simple algebraic extension $(L/K,v)$ of valued fields is the minimal length of the Mac Lane-Vaqui\'e 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.

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Enric Nart, Josnei Novacoski. 2025-03-24. Depth of Artin-Schreier defect towers. https://arxiv.org/abs/2503.18827

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