Zilber-Pink conjecture (original) (raw)
In mathematics, the Zilber–Pink conjecture is a far-reaching generalisation of many famous Diophantine conjectures and statements, such as André-Oort, Manin–Mumford, and Mordell-Lang. For algebraic tori and semiabelian varieties it was proposed by Boris Zilber and independently by Enrico Bombieri, David Masser, Umberto Zannier in the early 2000's. For semiabelian varieties the conjecture implies the Mordell-Lang and Manin-Mumford conjectures. Richard Pink proposed (again independently) a more general conjecture for Shimura varieties which also implies the André-Oort conjecture. In the case of algebraic tori, Zilber called it the Conjecture on Intersection with Tori (CIT). The general version is now known as the Zilber-Pink conjecture. It states roughly that atypical or unlikely intersectio
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| dbo:abstract | In mathematics, the Zilber–Pink conjecture is a far-reaching generalisation of many famous Diophantine conjectures and statements, such as André-Oort, Manin–Mumford, and Mordell-Lang. For algebraic tori and semiabelian varieties it was proposed by Boris Zilber and independently by Enrico Bombieri, David Masser, Umberto Zannier in the early 2000's. For semiabelian varieties the conjecture implies the Mordell-Lang and Manin-Mumford conjectures. Richard Pink proposed (again independently) a more general conjecture for Shimura varieties which also implies the André-Oort conjecture. In the case of algebraic tori, Zilber called it the Conjecture on Intersection with Tori (CIT). The general version is now known as the Zilber-Pink conjecture. It states roughly that atypical or unlikely intersections of an algebraic variety with certain special varieties are accounted for by finitely many special varieties. (en) |
| dbo:wikiPageExternalLink | https://books.google.com/books%3Fid=2dDneHOFx84C&pg=PA96 https://www.cambridge.org/gb/academic/subjects/mathematics/number-theory/point-counting-and-zilberpink-conjecture%3Fformat=HB&isbn=9781009170321 |
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| dbo:wikiPageWikiLink | dbr:Boris_Zilber dbr:David_Masser dbr:Algebraic_torus dbr:Umberto_Zannier dbc:Conjectures dbr:Mathematics dbr:Classical_modular_curve dbr:Enrico_Bombieri dbr:Arithmetic_of_abelian_varieties dbr:Complex_multiplication dbc:Diophantine_geometry dbr:Diophantine_geometry dbr:André-Oort_conjecture dbr:Semiabelian_variety dbr:Shimura_variety dbr:Mordell-Lang_conjecture |
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| dcterms:subject | dbc:Conjectures dbc:Diophantine_geometry |
| rdfs:comment | In mathematics, the Zilber–Pink conjecture is a far-reaching generalisation of many famous Diophantine conjectures and statements, such as André-Oort, Manin–Mumford, and Mordell-Lang. For algebraic tori and semiabelian varieties it was proposed by Boris Zilber and independently by Enrico Bombieri, David Masser, Umberto Zannier in the early 2000's. For semiabelian varieties the conjecture implies the Mordell-Lang and Manin-Mumford conjectures. Richard Pink proposed (again independently) a more general conjecture for Shimura varieties which also implies the André-Oort conjecture. In the case of algebraic tori, Zilber called it the Conjecture on Intersection with Tori (CIT). The general version is now known as the Zilber-Pink conjecture. It states roughly that atypical or unlikely intersectio (en) |
| rdfs:label | Zilber-Pink conjecture (en) |
| owl:sameAs | wikidata:Zilber-Pink conjecture https://global.dbpedia.org/id/GDDwh |
| prov:wasDerivedFrom | wikipedia-en:Zilber-Pink_conjecture?oldid=1117717108&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Zilber-Pink_conjecture |
| is dbo:wikiPageWikiLink of | dbr:André–Oort_conjecture |
| is foaf:primaryTopic of | wikipedia-en:Zilber-Pink_conjecture |