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Twists of symmetric bundles

Ph. Cassou-Nogues·B. Erez·M. J. Taylor
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Abstract

We establish comparison results between the Hasse-Witt invariants w_t(E) of a symmetric bundle E over a scheme and the invariants of one of its twists E_α. For general twists we describe the difference between w_t(E) and w_t(E_α) up to terms of degree 3. Next we consider a special kind of twist, which has been studied by A. Fröhlich. This arises from twisting by a cocycle obtained from an orthogonal representation. We show how to explicitly describe the twist for representations arising from very general tame actions. This involves the ``square root of the inverse different'' which Serre, Esnault, Kahn, Viehweg and ourselves had studied before. For torsors we show that, in our geometric set-up, Jardine's generalization of Frohlich's formula holds. The case of genuinely tamely ramified actions is geometrically more involved and leads us to introduce a ramification invariant which generalises in higher dimension the invariant introduced by Serre for curves.

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Ph. Cassou-Nogues, B. Erez, M. J. Taylor. 2004-04-11. Twists of symmetric bundles. https://arxiv.org/abs/math/0404219

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