Arithmetic properties of three-dimensional algebraic tori
Let K/k be an extension of degree 4 of an algebraic number field with the Galois group of its normal closure isomorphic to either alternating group \(A_ 4\) or \({\mathbb{Z}}/2\oplus {\mathbb{Z}}/2\). The author studies some arithmetical properties of 3-dimensional algebraic tori over k which are obtained as the kernel of the norm map \(N_{K/k}: R_{K/k}(G_ m)\to G_ m,\) where \(R_{K/k}\) is the Weil restriction functor. In particular, the author verifies for these tori the Hasse principle and the property of weak specialization.
scientific article; zbMATH DE number 3886047