For $L/K$, a cyclic unramified extension of number fields of a prime degree, Hilbert's Theorem 94 states that the order of the capitulation map is divisible by the degree of $L$ over $K$. In this talk, we present a generalization of Hilbert's Theorem 94, using the Brumer-Rosen-Zantema exact sequence (BRZ), a four-term sequence related to strongly ambiguous ideal classes in finite Galois extensions of number fields. Moreover, we show that the BRZ exact sequence can be readily used to obtain some known cohomological results in the literature concerning 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).

Bio: Abbas Maarefparvar got his Ph.D. in 2018 under the supervision of Ali Rajaei at the Tarbiat Modares University, Iran. Currently, he is a PIMS postdoctoral fellow at the University of Lethbridge. His main research area lies in algebraic number theory, especially the local-global class field theory, the Galois cohomology of number fields, and the arithmetic of elliptic curves.