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gptkbp:instanceOf
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gptkb:étale_fundamental_group
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gptkbp:actsOn
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algebraic numbers
\overline{\mathbb{Q}}
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gptkbp:category
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gptkb:algebra
gptkb:mathematics
gptkb:Galois_theory
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gptkbp:defines
|
the Galois group of the separable closure of the field of rational numbers over the rationals
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gptkbp:field
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\mathbb{Q}
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gptkbp:fullName
|
gptkb:absolute_Galois_group_of_the_rational_numbers
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gptkbp:importantFor
|
gptkb:algebraic_geometry
number theory
arithmetic geometry
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gptkbp:notation
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gptkb:Gal(\overline{\mathbb{Q}}/\mathbb{Q})
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gptkbp:openProblem
|
description of its structure
inverse Galois problem for \mathbb{Q}
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gptkbp:property
|
infinite
non-abelian
not fully understood
profinite topology
topologically finitely generated
has many finite quotients
every finite group is conjectured to be a Galois group over \mathbb{Q}
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gptkbp:relatedTo
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gptkb:Birch_and_Swinnerton-Dyer_conjecture
gptkb:Fermat's_Last_Theorem
gptkb:Frobenius_automorphism
gptkb:Langlands_program
gptkb:Serre's_conjecture
gptkb:Weil_group
gptkb:Tate_module
gptkb:étale_fundamental_group
gptkb:Kronecker–Weber_theorem
gptkb:Fontaine–Mazur_conjecture
gptkb:Iwasawa_theory
gptkb:inverse_Galois_problem
gptkb:Artin_reciprocity
gptkb:Grothendieck–Teichmüller_group
gptkb:Grothendieck's_anabelian_geometry
modular forms
class field theory
elliptic curves
Galois representations
local-global principle
motives
algebraic number fields
absolute Galois group of other fields
modular Galois representations
automorphisms of \overline{\mathbb{Q}}
field extensions of \mathbb{Q}
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gptkbp:structure
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gptkb:profinite_group
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gptkbp:bfsParent
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gptkb:Gal(\overline{\mathbb{Q}}/\mathbb{Q})
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gptkbp:bfsLayer
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8
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http://www.w3.org/2000/01/rdf-schema#label
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G \mathbb{Q}
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