Construction of Unramified Galois Extensions Over Maximal Abelian Extensions of Algebraic Number Fields

J. Math. Sci. Univ. Tokyo
Vol. 9 (2002), No. 3, Page 405--423.

Ohtani, Sachiko
Construction of Unramified Galois Extensions Over Maximal Abelian Extensions of Algebraic Number Fields
We construct unramified Galois extensions over maximal abelian extensions of algebraic number fields by using division points of abelian varieties which have everywhere semistable reduction. Further, by using division points of elliptic curves, we construct infinitely many linearly independent unramified Galois extensions of $\Qzi^{\ab}$ having $SL_2(\bZ_p)$ as the Galois group over $\Qzi^{\ab}$.