Pairs of symmetric bilinear forms in characteristic 2

William Charles Waterhouse

Vol. 69 (1977), No. 1, 275–283

DOI: 10.2140/pjm.1977.69.275

Abstract

The Grothendieck group of finite-length inner product modules over a PID is here shown to be a sum of countably many copies of the corresponding groups for the residue fields. It follows that nonsingular pairs of symmetric bilinear forms in characteristic 2 owe their extra complexity only to lack of a cancellation theorem: The invariants for isometry in other characteristics continue to determine classes in the Grothendieck group. This is also true for singular pairs.

Mathematical Subject Classification 2000

Primary: 10C05, 10C05

Secondary: 15A63

Milestones

Received: 6 July 1976

Published: 1 March 1977