A Remark on Transfers and Hyperbolicity

Abstract

In this note, we prove that the intersection of the kernels of two transfers map, involved in an exact sequence of Parimala, Sridharan and Suresh consists of the elements with order at most two. As an application, a new proof of a result of Scharlau stating that the torsion part of the Witt group of a central simple algebra with an involution of any kind is 2-primary is given.

Key Words:

• Witt group
• Hermitian form
• Central simple algebra with involution

2000 Mathematics Subject Classification:

• 16K20
• 11E39

Acknowledgment

The author gratefully acknowledges support from the RT Network “K-theory, Linear Algebraic Groups and Related Structures” (contract HPRN-CT-2002-00287).

Notes

^#Communicated by R. Parimala.