The main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes
نویسندگان
چکیده
We develop the plus/minus p-Selmer group theory and plus/minus padic L-function theory for an elliptic curve E with complex multiplication over an abelian extension F of the imaginary quadratic field K given by the complex multiplication of E when p is a prime inert over K/Q (i.e. supersingular). As a result, we prove that the characteristic ideal of the Pontryagin dual of the plus/minus p-Selmer group of E over the cyclotomic Zp-extension of F is generated by the plus/minus p-adic Lfunction of E. This work is a generalization of [12], [14], and [15].
منابع مشابه
The main conjecture for CM elliptic curves at supersingular primes
At a prime of ordinary reduction, the Iwasawa “main conjecture” for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the p-adic L-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is ...
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