TY - JOUR
T1 - The Local Correspondence over Absolute Fields
T2 - An Algebraic Approach
AU - Efrat, Ido
PY - 2000/12/1
Y1 - 2000/12/1
N2 - Let K,K′ be infinite fields which are finitely generated over their prime fields. Pop proved using model-theoretic methods that any isomorphism of the absolute Galois groups of K and K′ maps the decomposition groups of the Zariski prime divisors on K bijectively onto the decomposition groups of the Zariski prime divisors on K′ (relative to the separable closures). This was a main ingredient in his proof of the 0-dimensional case of Grothendieck's anabelian conjecture. In this paper we give a simplified and purely algebraic proof of this fact.
AB - Let K,K′ be infinite fields which are finitely generated over their prime fields. Pop proved using model-theoretic methods that any isomorphism of the absolute Galois groups of K and K′ maps the decomposition groups of the Zariski prime divisors on K bijectively onto the decomposition groups of the Zariski prime divisors on K′ (relative to the separable closures). This was a main ingredient in his proof of the 0-dimensional case of Grothendieck's anabelian conjecture. In this paper we give a simplified and purely algebraic proof of this fact.
UR - http://www.scopus.com/inward/record.url?scp=0347016056&partnerID=8YFLogxK
U2 - 10.1155/S107379280000060X
DO - 10.1155/S107379280000060X
M3 - Article
AN - SCOPUS:0347016056
SN - 1073-7928
VL - 2000
SP - 1213
EP - 1223
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 23
ER -