absolute Galois group of Q

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Weyl_group profinite group
gptkbp:actsOn	algebraic numbers
gptkbp:automorphismGroup	algebraic closure of Q
gptkbp:contains	complex conjugation decomposition groups inertia subgroups
gptkbp:defines	Galois group of the algebraic closure of Q over Q
gptkbp:field	rational numbers
gptkbp:finite_quotients_correspond_to	finite Galois extensions of Q
https://www.w3.org/2000/01/rdf-schema#label	absolute Galois group of Q
gptkbp:importantFor	gptkb:algebraic_geometry number theory arithmetic geometry
gptkbp:notation	Gal(\\overline{\\mathbb{Q}}/\\mathbb{Q})
gptkbp:open_subgroups_correspond_to	finite Galois extensions of Q
gptkbp:profinite	true
gptkbp:relatedTo	gptkb:absolute_Galois_group_of_finite_fields gptkb:Frobenius_automorphism gptkb:Langlands_program gptkb:Tate_module gptkb:Kronecker–Weber_theorem gptkb:motivic_Galois_group gptkb:inverse_Galois_problem gptkb:Artin_reciprocity gptkb:anabelian_geometry gptkb:Mochizuki's_inter-universal_Teichmüller_theory gptkb:Grothendieck–Teichmüller_group algebraic number theory modular forms class field theory Galois representations field extensions absolute Galois group of function fields absolute Galois group of local fields cyclotomic character profinite completion of free group (conjecturally) profinite group theory étale fundamental group of Spec(Q)
gptkbp:structure	unknown
gptkbp:topology	profinite topology
gptkbp:bfsParent	gptkb:Galois_group_of_the_rationals
gptkbp:bfsLayer	7