Mazur's control theorem

Short description: Describes the behavior in Zp extensions of the Selmer group of an abelian variety

In number theory, Mazur's control theorem, introduced by Mazur (1972), describes the behavior in Z_p extensions of the Selmer group of an abelian variety over a number field.

References

• Mazur, Barry (1972), "Rational points of abelian varieties with values in towers of number fields", Inventiones Mathematicae 18 (3–4): 183–266, doi:10.1007/BF01389815, ISSN 0020-9910, Bibcode: 1972InMat..18..183M