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arXiv · 2209.08634

Divided powers in the Witt ring of symmetric bilinear forms

Burt Totaro
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Abstract

The Witt ring of symmetric bilinear forms over a field has divided power operations. On the other hand, it follows from Garibaldi-Merkurjev-Serre's work on cohomological invariants that all operations on the Witt ring are essentially 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.

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Burt Totaro. 2022-09-18. Divided powers in the Witt ring of symmetric bilinear forms. https://doi.org/10.2140/akt.2023.8.275

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