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Metric groups attached to skew-symmetric biextensions

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Abstract

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 \(\mathbb{Q}_{p}/\mathbb{Z}_{p}\). 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 \(\mathbb{G}_{a}\), 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).

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  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Swarnendu Datta

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  1. Swarnendu Datta
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Correspondence to Swarnendu Datta.

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Datta, S. Metric groups attached to skew-symmetric biextensions. Transformation Groups 15, 72–91 (2010). https://doi.org/10.1007/s00031-010-9078-5

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