TY - JOUR
T1 - Abelian absolute Galois groups In Erinnerung an Wulf-Dieter Geyer (1939–2019)
AU - Jarden, Moshe
N1 - Publisher Copyright:
© The Author(s), 2024.
PY - 2024/5/1
Y1 - 2024/5/1
N2 - 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).
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).
KW - Absolute Galois Group
KW - Henselian Fields
UR - http://www.scopus.com/inward/record.url?scp=85184508269&partnerID=8YFLogxK
U2 - 10.1017/S0017089524000028
DO - 10.1017/S0017089524000028
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AN - SCOPUS:85184508269
SN - 0017-0895
VL - 66
SP - 359
EP - 367
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
IS - 2
ER -