The Other Group of as Galois Extension
Lex E. Renner

TL;DR
This paper constructs a canonical subgroup scheme associated with a Galois extension, revealing that it is constant precisely when the Galois group is abelian, thus linking group scheme structure to classical Galois theory.
Contribution
It introduces a canonical subgroup scheme for Galois extensions, providing a new perspective on the relationship between Galois groups and automorphism group schemes.
Findings
The subgroup scheme is constant if and only if the Galois group is abelian.
When Galois group is abelian, the subgroup scheme coincides with the Galois group.
The construction offers a canonical way to associate group schemes to Galois extensions.
Abstract
Let be a finite Galois extension of fields with Galois group . Let be the automorphism -group scheme of . We construct a canonical -subgroup scheme with the property that is a -torsor for . is a constant -group if and only if is abelian, in which case .
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Advanced Mathematical Identities
