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- Manin_obstruction abstract "In mathematics, in the field of arithmetic algebraic geometry, the Manin obstruction (named after Yuri Manin) is attached to a geometric object X which measures the failure of the Hasse principle for X: that is, if the value of the obstruction is non-trivial, then X may have points over all local fields but not over a global field.For abelian varieties the Manin obstruction is just the Tate-Shafarevich group and fully accounts for the failure of the local-to-global principle (under the assumption that the Tate-Shafarevich group is finite). There are however examples, due to Skorobogatov, of varieties with trivial Manin obstruction which have points everywhere locally and yet no global points.".
- Manin_obstruction wikiPageID "18960214".
- Manin_obstruction wikiPageLength "1612".
- Manin_obstruction wikiPageOutDegree "12".
- Manin_obstruction wikiPageRevisionID "552062641".
- Manin_obstruction wikiPageWikiLink Abelian_variety.
- Manin_obstruction wikiPageWikiLink Alexei_Skorobogatov.
- Manin_obstruction wikiPageWikiLink Cambridge_University_Press.
- Manin_obstruction wikiPageWikiLink Category:Diophantine_geometry.
- Manin_obstruction wikiPageWikiLink Global_field.
- Manin_obstruction wikiPageWikiLink Hasse_principle.
- Manin_obstruction wikiPageWikiLink Inventiones_Mathematicae.
- Manin_obstruction wikiPageWikiLink Local_field.
- Manin_obstruction wikiPageWikiLink Mathematics.
- Manin_obstruction wikiPageWikiLink Springer_Science+Business_Media.
- Manin_obstruction wikiPageWikiLink Tate–Shafarevich_group.
- Manin_obstruction wikiPageWikiLink Yuri_Manin.
- Manin_obstruction wikiPageWikiLinkText "Manin obstruction".
- Manin_obstruction wikiPageUsesTemplate Template:Cite_book.
- Manin_obstruction wikiPageUsesTemplate Template:Cite_journal.
- Manin_obstruction wikiPageUsesTemplate Template:Geometry-stub.
- Manin_obstruction wikiPageUsesTemplate Template:Numtheory-stub.
- Manin_obstruction subject Category:Diophantine_geometry.
- Manin_obstruction comment "In mathematics, in the field of arithmetic algebraic geometry, the Manin obstruction (named after Yuri Manin) is attached to a geometric object X which measures the failure of the Hasse principle for X: that is, if the value of the obstruction is non-trivial, then X may have points over all local fields but not over a global field.For abelian varieties the Manin obstruction is just the Tate-Shafarevich group and fully accounts for the failure of the local-to-global principle (under the assumption that the Tate-Shafarevich group is finite). ".
- Manin_obstruction label "Manin obstruction".
- Manin_obstruction sameAs Q6749775.
- Manin_obstruction sameAs m.04jd21r.
- Manin_obstruction sameAs Q6749775.
- Manin_obstruction wasDerivedFrom Manin_obstruction?oldid=552062641.
- Manin_obstruction isPrimaryTopicOf Manin_obstruction.