UC Santa Barbara

In this paper, we study linked bilinear pairings and their associated Witt rings. An open problem is to classify all linked quaterionic pairings. The Elementary Type Conjecture [1] asserts that every finite linked quaternionic pairing can be built from symplectic pairings using direct sums and group extensions iteratively. We investigate the validity of this conjecture by studying an infinite quaternionic pairing and its sub- pairings motivated by certain structures arising in Henselian dyadic valued fields.