Short Proofs For Some Known Cohomological Results

In this talk, we first introduce the Brumer-Rosen-Zantema exact sequence (BRZ), a four-term sequence related to strongly ambiguous ideal classes in finite Galois extensions of number fields. Then, using BRZ, we obtain some known cohomological results in the literature concerning Hilbert's Theorem 94, the capitulation map, and the Principal Ideal Theorem. This is a joint work with Ali Rajaei (Tarbiat Modares University) and Ehsan Shahoseini (Institute for Research in Fundamental Sciences).