Linkage of Pfister forms over semi-global fields.

We study linkage of (d + 1) -fold quadratic Pfister forms over function fields in one variable over a henselian valued field of 2-cohomological dimension d. Specifically, we characterise this property in terms of linkage of quadratic Pfister forms over function fields over the residue field of the henselian valued field; in full generality in characteristic different from 2, and for most complete discretely valued fields in characteristic 2. As an application, we obtain a proof that (d + 2) -fold quadratic Pfister forms over function fields in one variable over a d-dimensional higher local field are linked. [ABSTRACT FROM AUTHOR]