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- Semistable_abelian_variety abstract "In algebraic geometry, a semistable abelian variety is an abelian variety defined over a global or local field, which is characterized by how it reduces at the primes of the field.For an abelian variety A defined over a field F 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 overSpec(R)(cf. spectrum of a ring) for which the generic fibre constructed by means of the morphismSpec(F) → Spec(R)gives back A. The Néron model is a smooth group scheme, so we can consider A0, the connected component of the Néron model which contains the identity for the group law. This is an open subgroup scheme of the Néron model. For a residue field k, A0k is a group variety over k, hence an extension of an abelian variety by a linear group. If this linear group is an algebraic torus, so that A0k is a semiabelian variety, then A has semistable reduction at the prime corresponding to k. If F is global, then A is semistable if it has good or semistable reduction at all primes.The semistable reduction theorem of Alexander Grothendieck states that an abelian variety acquires semistable reduction over a finite extension of F.".
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- Semistable_abelian_variety wikiPageLength "4048".
- Semistable_abelian_variety wikiPageOutDegree "36".
- Semistable_abelian_variety wikiPageRevisionID "669771980".
- Semistable_abelian_variety wikiPageWikiLink Abelian_variety.
- Semistable_abelian_variety wikiPageWikiLink Alexander_Grothendieck.
- Semistable_abelian_variety wikiPageWikiLink Algebraic_geometry.
- Semistable_abelian_variety wikiPageWikiLink Algebraic_group.
- Semistable_abelian_variety wikiPageWikiLink Algebraic_torus.
- Semistable_abelian_variety wikiPageWikiLink Bad_reduction.
- Semistable_abelian_variety wikiPageWikiLink Category:Abelian_varieties.
- Semistable_abelian_variety wikiPageWikiLink Category:Diophantine_geometry.
- Semistable_abelian_variety wikiPageWikiLink Category:Elliptic_curves.
- Semistable_abelian_variety wikiPageWikiLink Characteristic_(algebra).
- Semistable_abelian_variety wikiPageWikiLink Cusp_(singularity).
- Semistable_abelian_variety wikiPageWikiLink Double_point.
- Semistable_abelian_variety wikiPageWikiLink Elliptic_curve.
- Semistable_abelian_variety wikiPageWikiLink Empty_set.
- Semistable_abelian_variety wikiPageWikiLink Finite_set.
- Semistable_abelian_variety wikiPageWikiLink Fixed_point_(mathematics).
- Semistable_abelian_variety wikiPageWikiLink Generic_fibre.
- Semistable_abelian_variety wikiPageWikiLink Generic_point.
- Semistable_abelian_variety wikiPageWikiLink Global_field.
- Semistable_abelian_variety wikiPageWikiLink Glossary_of_arithmetic_and_Diophantine_geometry.
- Semistable_abelian_variety wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Semistable_abelian_variety wikiPageWikiLink Group_scheme.
- Semistable_abelian_variety wikiPageWikiLink Group_variety.
- Semistable_abelian_variety wikiPageWikiLink Local_field.
- Semistable_abelian_variety wikiPageWikiLink Mathematical_singularity.
- Semistable_abelian_variety wikiPageWikiLink Modular_arithmetic.
- Semistable_abelian_variety wikiPageWikiLink Morphism.
- Semistable_abelian_variety wikiPageWikiLink Multiplicative_bad_reduction.
- Semistable_abelian_variety wikiPageWikiLink Non-empty_set.
- Semistable_abelian_variety wikiPageWikiLink Néron_model.
- Semistable_abelian_variety wikiPageWikiLink Prime_field.
- Semistable_abelian_variety wikiPageWikiLink Prime_number.
- Semistable_abelian_variety wikiPageWikiLink Rational_number.
- Semistable_abelian_variety wikiPageWikiLink Residue_field.
- Semistable_abelian_variety wikiPageWikiLink Ring_of_integers.
- Semistable_abelian_variety wikiPageWikiLink Ruth_Lawrence.
- Semistable_abelian_variety wikiPageWikiLink Scheme_(mathematics).
- Semistable_abelian_variety wikiPageWikiLink Semiabelian_variety.
- Semistable_abelian_variety wikiPageWikiLink Singularity_(mathematics).
- Semistable_abelian_variety wikiPageWikiLink Spectrum_of_a_ring.
- Semistable_abelian_variety wikiPageWikiLink Springer-Verlag.
- Semistable_abelian_variety wikiPageWikiLink Springer_Science+Business_Media.
- Semistable_abelian_variety wikiPageWikiLink Tates_algorithm.
- Semistable_abelian_variety wikiPageWikiLinkText "Semistable abelian variety".
- Semistable_abelian_variety wikiPageWikiLinkText "Semistable abelian variety#Semistable elliptic curve".
- Semistable_abelian_variety wikiPageWikiLinkText "semistable abelian variety".
- Semistable_abelian_variety wikiPageWikiLinkText "semistable reduction".
- Semistable_abelian_variety hasPhotoCollection Semistable_abelian_variety.
- Semistable_abelian_variety wikiPageUsesTemplate Template:Cite_book.
- Semistable_abelian_variety wikiPageUsesTemplate Template:Reflist.
- Semistable_abelian_variety subject Category:Abelian_varieties.
- Semistable_abelian_variety subject Category:Diophantine_geometry.
- Semistable_abelian_variety subject Category:Elliptic_curves.
- Semistable_abelian_variety hypernym Variety.
- Semistable_abelian_variety type Grape.
- Semistable_abelian_variety type Group.
- Semistable_abelian_variety type Field.
- Semistable_abelian_variety type Function.
- Semistable_abelian_variety type Group.
- Semistable_abelian_variety type Variety.
- Semistable_abelian_variety comment "In algebraic geometry, a semistable abelian variety is an abelian variety defined over a global or local field, which is characterized by how it reduces at the primes of the field.For an abelian variety A defined over a field F 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 overSpec(R)(cf.".
- Semistable_abelian_variety label "Semistable abelian variety".
- Semistable_abelian_variety sameAs m.03mywm.
- Semistable_abelian_variety sameAs Q7449666.
- Semistable_abelian_variety sameAs Q7449666.
- Semistable_abelian_variety wasDerivedFrom Semistable_abelian_variety?oldid=669771980.
- Semistable_abelian_variety isPrimaryTopicOf Semistable_abelian_variety.