The u-invariant and the symbol length in Kato-Milne cohomology

Various connections between the u-invariant of a field and the symbol length in Milnor K-theory and Kato-Milne cohomology have been proven in recent years.

Karshen and Saltman have each proven independently that when the characteristic is different from 2, the finiteness of the u-invariant implies the finiteness of the symbol length in all Milnor K-groups.

We present the analogous result in the case of characteristic two.

Unlike the previous case, in this case we are able to provide an explicit upper bound for the symbol length.

The talk is based on joint work with Kelly McKinnie.