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- Conductor_of_an_abelian_variety abstract "In mathematics, in Diophantine geometry, the conductor of an abelian variety defined over a local or global field F is a measure of how "bad" the bad reduction at some prime is. It is connected to the ramification in the field generated by the torsion points.For an abelian variety A defined over a field F as above, with ring of integers R, consider the Néron model of A, which is a 'best possible' model of A defined over R. This model may be represented as a scheme over Spec(R)(cf. spectrum of a ring) for which the generic fibre constructed by means of the morphismSpec(F) → Spec(R)gives back A. Let A0 denote the open subgroup scheme of the Néron model whose fibres are the connected components. For a maximal ideal P of A with residue field k, A0k is a group variety over k, hence an extension of an abelian variety by a linear group. This linear group is an extension of a torus by a unipotent group. Let uP be the dimension of the unipotent group and tP the dimension of the torus. The order of the conductor at P iswhere is a measure of wild ramification. When F is a number field, the conductor ideal of A is given by".
- Conductor_of_an_abelian_variety wikiPageID "18847878".
- Conductor_of_an_abelian_variety wikiPageRevisionID "511217917".
- Conductor_of_an_abelian_variety hasPhotoCollection Conductor_of_an_abelian_variety.
- Conductor_of_an_abelian_variety subject Category:Abelian_varieties.
- Conductor_of_an_abelian_variety subject Category:Algebraic_number_theory.
- Conductor_of_an_abelian_variety subject Category:Diophantine_geometry.
- Conductor_of_an_abelian_variety type AbelianVarieties.
- Conductor_of_an_abelian_variety type Abstraction100002137.
- Conductor_of_an_abelian_variety type Assortment108398773.
- Conductor_of_an_abelian_variety type Attribute100024264.
- Conductor_of_an_abelian_variety type Collection107951464.
- Conductor_of_an_abelian_variety type Curve113867641.
- Conductor_of_an_abelian_variety type EllipticCurves.
- Conductor_of_an_abelian_variety type Group100031264.
- Conductor_of_an_abelian_variety type Line113863771.
- Conductor_of_an_abelian_variety type Shape100027807.
- Conductor_of_an_abelian_variety comment "In mathematics, in Diophantine geometry, the conductor of an abelian variety defined over a local or global field F is a measure of how "bad" the bad reduction at some prime is. It is connected to the ramification in the field generated by the torsion points.For an abelian variety A defined over a field F as above, with ring of integers R, consider the Néron model of A, which is a 'best possible' model of A defined over R. This model may be represented as a scheme over Spec(R)(cf.".
- Conductor_of_an_abelian_variety label "Conductor of an abelian variety".
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- Conductor_of_an_abelian_variety sameAs Q5159399.
- Conductor_of_an_abelian_variety sameAs Q5159399.
- Conductor_of_an_abelian_variety sameAs Conductor_of_an_abelian_variety.
- Conductor_of_an_abelian_variety wasDerivedFrom Conductor_of_an_abelian_variety?oldid=511217917.
- Conductor_of_an_abelian_variety isPrimaryTopicOf Conductor_of_an_abelian_variety.