Abelian absolute Galois groups In Erinnerung an Wulf-Dieter Geyer (1939–2019)

Moshe Jarden

doi:10.1017/S0017089524000028

Abelian absolute Galois groups In Erinnerung an Wulf-Dieter Geyer (1939–2019)

Moshe Jarden^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Generalizing a result of Wulf-Dieter Geyer in his thesis, we prove that if K is a finitely generated extension of transcendence degree r of a global field and A is a closed abelian subgroup of Gal(K), then rank(A) ≤ r + 1. Moreover, if char(K) = 0, then Ẑr+¹ is isomorphic to a closed subgroup of Gal(K).

Original language	English
Pages (from-to)	359-367
Number of pages	9
Journal	Glasgow Mathematical Journal
Volume	66
Issue number	2
DOIs	https://doi.org/10.1017/S0017089524000028
State	Published - 1 May 2024

Keywords

Absolute Galois Group
Henselian Fields

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10.1017/S0017089524000028

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abstract = "Generalizing a result of Wulf-Dieter Geyer in his thesis, we prove that if K is a finitely generated extension of transcendence degree r of a global field and A is a closed abelian subgroup of Gal(K), then rank(A) ≤ r + 1. Moreover, if char(K) = 0, then Ẑr+1 is isomorphic to a closed subgroup of Gal(K).",

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AB - Generalizing a result of Wulf-Dieter Geyer in his thesis, we prove that if K is a finitely generated extension of transcendence degree r of a global field and A is a closed abelian subgroup of Gal(K), then rank(A) ≤ r + 1. Moreover, if char(K) = 0, then Ẑr+1 is isomorphic to a closed subgroup of Gal(K).

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KW - Henselian Fields

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Abelian absolute Galois groups In Erinnerung an Wulf-Dieter Geyer (1939–2019)

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