Download this article
 Download this article For screen
For printing
Recent Issues
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Divided powers in the Witt ring of symmetric bilinear forms

Burt Totaro

Vol. 8 (2023), No. 2, 275–284

The Witt ring of symmetric bilinear forms over a field has divided power operations. On the other hand, it follows from Garibaldi, Merkurjev, and Serre’s work on cohomological invariants that all operations on the Witt ring are linear combinations of exterior powers. We find the explicit formula for the divided powers as a linear combination of exterior powers. The coefficients involve the “tangent numbers”, related to Bernoulli numbers. The divided powers on the Witt ring give another construction of the divided powers on Milnor K-theory modulo  2.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Witt ring, symmetric bilinear forms, quadratic forms, divided powers
Mathematical Subject Classification
Primary: 11E81
Secondary: 11B68, 19D45
Received: 21 September 2022
Revised: 13 April 2023
Accepted: 14 April 2023
Published: 14 June 2023
Burt Totaro
Mathematics Department
University of California
Los Angeles, CA
United States