Some remarks on the generation of subfields of ring class fields (Q1112106)

The author announces a result on the generation of the n-th layer \(K_ n\) of the anticyclotomic \({\mathbb{Z}}_ p\)-extension of an imaginary quadratic number field K. If p is an odd prime, \({\mathfrak O}_ n\) denotes the order of K of conductor \(p^ n\), then \(K_ n=K(N_{L_ n| K_ n}(\epsilon^ s_ n))\), \(s=1,2,3,...\), where \(L_ n=K(j({\mathfrak O}_ n))\) is the ring class field corresponding to \({\mathfrak O}_ n\) and \(\epsilon_ n\) is a Siegel unit. No proofs are given.