Seminar

The solution of the Milnor conjectures on quadratic forms provides a complete set of invariants for quadratic forms. One would like to use this classification to attack a classical problem on the u-invariant of function fields of curves over totally imaginary number fields. The u-invariant is the maximum dimension of anisotropic quadratic forms over a field. Even finiteness is not known in this case. We explain how the finiteness of the u-invariant is reduced to bounding indices of the unramified Brauer group of the field. We run through the history and state some results in this direction.