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#### Seminar der Forschergruppe 'Symmetrie, Geometrie und Arithmetik'

„Vanishing of a $\mu$-invariant and the weak Leopoldt conjecture for a non-cyclotomic $Z_2$ extension“
Dr. Yukako Kezuka, Universität Regensburg

Take $q$ to be any prime number congruent to $7$ modulo $8$, and let $K=Q(sqrt{-q})$. The prime $2$ splits in $K$, and we take $\mathfrak{p}$ to be one of the primes of $K$ above $2$. Let $H$ be the Hilbert class field of $K$ and write $K_\infty$ for the unique $Z_2$-extension of $K$ unramified outside $\mathfrak{p}$. We will show, by proving an analogue of Iwasawa's $\mu=0$ conjecture, that the weak $\mathfrak{p}$-adic Leopoldt conjecture holds for the compositum $J_\infty=JK_\infty$ for an arbitrary quadratic extension $J$ of $H$. This is a joint work with J. Choi and Y. Li.

Freitag, den 25. Januar 2019 um 13:30 Uhr, in INF 205, SR A Freitag, den 25. Januar 2019 at 13:30, in INF 205, SR A

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Dr. Michael Fütterer