P-adic algebraic-concordance obstruction

Extending an algebraic-concordance class from $\mathbb{Q}$ to a p-adic field ${\mathbb{Q}}_p$ detects torsion invisible over the real numbers. For $p\equiv 3(\mathrm{mod}4)$, an odd-dimensional second-residue form generates the order-four part of the local Witt group.