Abstract

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  $2$.

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