Iwasawa Theory for Elliptic Curves
نویسنده
چکیده
The topics that we will discuss have their origin in Mazur’s synthesis of the theory of elliptic curves and Iwasawa’s theory of ZZp-extensions in the early 1970s. We first recall some results from Iwasawa’s theory. Suppose that F is a finite extension of Q and that F∞ is a Galois extension of F such that Gal(F∞/F ) ∼= ZZp, the additive group of p-adic integers, where p is any prime. Equivalently, F∞ = ⋃ n≥0 Fn, where, for n ≥ 0, Fn is a cyclic extension of F of degree p and F = F0 ⊂ F1 ⊂ · · · ⊂ Fn ⊂ Fn+1 ⊂ · · · . Let hn denote the class number of Fn, p en the exact power of p dividing hn. Then Iwasawa proved the following result.
منابع مشابه
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تاریخ انتشار 1999