Room 202, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 202室)

Analogues of Iwasawa’s µ = 0 conjecture and the weak Leopoldt conjecture for a non-cyclotomic Z2-extension

Junhwa Choi (
Pohang University of Science and Technology
)

Abstract

Let K = Q( √ −q), where q is any prime with q ≡ 7 mod 8, and write O for the ring of integers of K. The prime 2 splits in K, say 2O = pp∗ , and there is a unique Z2-extension K∞ of K unramified outside p. Let J be an arbitrary quadratic extension of the Hilbert class field H of K, and write J∞ = JK∞. We stress that J is not in general abelian over K. In this talk, we will prove the analogues of Iwasawa’s µ = 0 conjecture and the weak Leopoldt conjecture for the extension J∞/J. This is joint work with Yukako Kezuka and Yongxiong Li.