Metric groups attached to skew-symmetric biextensions

Let G be a commutative, unipotent, perfect, connected group scheme over an algebraically closed field of characteristic p > 0 and let E be a biextension of G × G by the discrete group \mathbbQ_p/\mathbbZ_p\mathbb{Q}_{p}/\mathbb{Z}_{p}. When E is skew-symmetric, V. Drinfeld defined a certain metric group A associated to E (when G is the perfectization of the additive group \mathbbG_a\mathbb{G}_{a}, it is easy to compute this metric group, cf. Appendix A). In this paper we prove a conjecture due to Drinfeld about the class of the metric group A in the Witt group (cf. Appendix B).