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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:abbreviation
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gptkb:Sha
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gptkbp:appearsIn
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gptkb:Birch_and_Swinnerton-Dyer_conjecture
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gptkbp:containsElement
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isomorphism class of torsors
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gptkbp:defines
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The Tate-Shafarevich group of an abelian variety A over a number field K is the group of principal homogeneous spaces for A over K that become trivial over every completion of K.
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gptkbp:field
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gptkb:algebraic_geometry
number theory
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https://www.w3.org/2000/01/rdf-schema#label
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Tate-Shafarevich group
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gptkbp:introducedIn
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1960s
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gptkbp:namedAfter
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gptkb:Igor_Shafarevich
gptkb:John_Tate
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gptkbp:openProblem
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Finiteness of the Tate-Shafarevich group for elliptic curves over number fields
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gptkbp:relatedTo
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gptkb:algebraic_geometry
gptkb:Galois_cohomology
gptkb:elliptic_curve
principal homogeneous space
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gptkbp:symbol
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Ш
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gptkbp:bfsParent
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gptkb:Tate's_theorem_on_the_Galois_cohomology_of_elliptic_curves
gptkb:Selmer_group_of_abelian_varieties
gptkb:n-Selmer_group
gptkb:p-Selmer_group
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gptkbp:bfsLayer
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7
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