Mazur's control theorem, introduced by Barry Mazur in a 1972 paper in Inventiones Mathematicae titled Rational points of abelian varieties with values in towers of number fields, describes the behavior of the Selmer group of an abelian variety over a number field within its Z_p extensions. The Wikipedia article on the theorem is itself a stub, so beyond this core statement its fuller significance within Iwasawa theory is not yet documented in the one source read for this description.
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Statement FormCharacterization Theorem 1 Mazur's Control Theorem
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Source Mazur's control theorem (Wikipedia)
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1. Mazur's control theorem (Wikipedia)
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introduced by Mazur (1972)
Principal Result Of: Barry Mazur, Lead sentence of the article on the result
In number theory, Mazur's control theorem, introduced by Mazur (1972), describes the behavior in Zp extensions of the Selmer group of an abelian variety over a number field.
In Branch: Number Theory, Lead sentence
In number theory, Mazur's control theorem, introduced by Mazur (1972), describes the behavior in Zp extensions of the Selmer group
Proved By: Barry Mazur, Lead sentence, attribution
introduced by Mazur (1972)
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