Artin-Schreier extensions in NIP and simple fields
Itay Kaplan, Thomas Scanlon, Frank O. Wagner
TL;DR
This paper proves that NIP fields cannot have Artin-Schreier extensions and that simple fields have only finitely many such extensions, revealing structural properties of these fields.
Contribution
It establishes new results linking model-theoretic properties of fields with their algebraic extensions, specifically in NIP and simple fields.
Findings
NIP fields have no Artin-Schreier extensions
Simple fields have finitely many Artin-Schreier extensions
Provides insights into the structure of fields with model-theoretic restrictions
Abstract
We show that NIP fields have no Artin-Schreier extension, and that simple fields have only a finite number of them.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology