Year: 2025
Type: preprint
Abstract: Consider a simple algebraic valued field extension $(L/K,v)$ and denote by $\VR_L$ and $\VR_K$ the corresponding valuation rings. The main goal of this paper is to present, under certain assumptions, a description of $\VR_L$ in terms of generators and relations over $\VR_K$. The main tool used here are complete sequences of key polynomials. It is known that if the ramification index of $(L/K,v)$ is one, then every complete set gives rise to a set of generators of $\VR_L$ over $\VR_K$. We show that we can find a sequence of key polynomials for $(L/K,v)$ which satisfies good properties (called neat). Then we present explicit ``neat" relations that generate all the relations between the corresponding generators of $\VR_L$ over $\VR_K$.
Source: arXiv (Cornell University)
Authors: Novacoski, Josnei, Spivakovsky, Mark
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6948499267
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