On Generalised Albert Forms over Discretely Valued Fields

For a discrete valuation ring R with quotient field K and residue field F both of characteristic not 2, we study low-dimensional quadratic forms with Witt class in the n-th power of the fundamental ideal of F resp. K and point out connections between forms over these fields. We analyse the minimal number of Pfister forms such that a given form is Witt equivalent to the sum of these and study forms congruent modulo a higher power of the fundamental ideal towards similarity.