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Divided powers in the
Witt ring of symmetric bilinear forms
Burt Totaro |
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Vol. 8 (2023), No. 2, 275–284
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Abstract |
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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 -theory modulo . |
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Keywords
Witt ring, symmetric bilinear forms, quadratic forms,
divided powers
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Mathematical Subject Classification
Primary: 11E81
Secondary: 11B68, 19D45
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Milestones
Received: 21 September 2022
Revised: 13 April 2023
Accepted: 14 April 2023
Published: 14 June 2023
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Authors |
| Burt Totaro | |
| Mathematics Department University of California Los Angeles, CA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
