The corestriction of valued division algebras over Henselian fields. I

Yoon Sung Hwang

Vol. 170 (1995), No. 1, 53–81

DOI: 10.2140/pjm.1995.170.53

Abstract

When L∕F is an unramified extension of Henselian fields, we analyze the underlying division algebra ^cD of the corestriction cor_L∕F(D) of a tame division algebra D over L with respect to the unique valuations on ^cD and D extending the valuations on F and L. We show that the value group of ^cD lies in the value group of D and for the center of residue division algebra, Z(^cD) ⊆𝒩(Z(D)∕F)^1∕k, where 𝒩(Z(D)∕F) is the normal closure of Z(D) over F and k is an integer depending on which roots of unity lie in F and L.

Mathematical Subject Classification 2000

Primary: 12E15

Secondary: 12J10, 16K20

Milestones

Received: 10 November 1992

Revised: 8 April 1993

Published: 1 September 1995