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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. ==References== * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Manin obstruction」の詳細全文を読む スポンサード リンク
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