Discriminants of involutions on Henselian division algebras

Maurice Chacron, H. Dherte, Jean-Pierre Tignol, Adrian R. Wadsworth and V. I. Yanchevskiĭ

Vol. 167 (1995), No. 1, 49–79

DOI: 10.2140/pjm.1995.167.49

Abstract

The discriminant of an involution of the first kind on a finite-dimensional division algebra over a field with a Henselian valuation of residue characteristic different from 2 is computed in terms of residue information. We also describe the set of discriminants of involutions on such division algebras. In the case where the residue involution is the identity, a stable decomposition of the division algebra into the tensor product of a semi-ramified and a totally ramified subalgebra is obtained.

Mathematical Subject Classification 2000

Primary: 16K20

Secondary: 12E15, 12J25

Milestones

Received: 9 June 1992

Revised: 1 October 1992

Published: 1 January 1995