Kezuka, Yukako (2019) On the main conjecture of Iwasawa theory for certain non-cyclotomic Zp-extensions. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 100 (1). pp. 107-136. ISSN 0024-6107, 1469-7750
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Let K=Q(-q), where q is any prime number congruent to 7 modulo 8, with ring of integers O and Hilbert class field H. Suppose p does not divide [H:K] is a prime number which splits in K, say pO=pp*. Let H infinity=HK infinity, where K infinity is the unique Zp-extension of K unramified outside p. Write M(H infinity) for the maximal abelian p-extension of H infinity unramified outside the primes above p, and set X(H infinity)=Gal(M(H infinity)/H infinity). In this paper, we establish the main conjecture of Iwasawa theory for the Iwasawa module X(H infinity). As a consequence, we have that if X(H infinity)=0, the relevant L-values are p-adic units. In addition, the main conjecture for X(H infinity) has implications towards (a) the BSD Conjecture for a class of CM elliptic curves; (b) weak p-adic Leopoldt conjecture.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ADIC L-FUNCTIONS; ELLIPTIC-CURVES; COMPLEX MULTIPLICATION; 11R23 (primary) |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Guido Kings |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Apr 2020 07:08 |
| Last Modified: | 01 Apr 2020 07:08 |
| URI: | https://pred.uni-regensburg.de/id/eprint/26552 |
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