A genus formula for the positive étale wild kernel

Abstract

Let F be a number field and let i ≥ 2 be an integer. In this paper, we study the positive étale wild kernel WK ét,+ 2i−2 F , which is the twisted analogue of the 2-primary part of the narrow class group. If E/F is a Galois extension of number fields with Galois group G, we prove a genus formula relating the order of the groups (WK ét,+ 2i−2 E) G and WK ét,+ 2i−2 F .2010 Mathematics Subject Classification. 11R34, 11R70.