The Growth of Selmer Ranks of an Abelian Variety with Complex Multiplication
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چکیده
Let K be a CM field and O be its ring of integers. Let p be an odd prime integer and p be a prime in K lying above p. Let F be a Galois extension of K unramified over p. For an Abelian variety A defined over F with complex multiplication by O, we study the variation of the p-ranks of the Selmer groups in pro-p algebraic extensions. We first study the Zpextension case. When K is quadratic imaginary and E is an elliptic curve, we also study the p-ranks of the Selmer groups in an unramified p-class field tower.
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تاریخ انتشار 2006