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Descent of vector bundles under wildly ramified extensions

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Abstract

Given an irreducible normal Noetherian scheme and a finite Galois extension of the field of rational functions, we discuss the comparison of the categories of vector bundles on the scheme and equivariant vector bundles on the integral closure in the extension. This is well understood in the tame case (geometric stabilizer groups of order invertible in the local rings), so we focus on the wild (non-tame) case, which may be reduced to the case of cyclic extensions of prime order. In this case, under an additional flatness hypothesis, we give a characterization of the equivariant vector bundles that arise by base change from vector bundles on the scheme.

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Acknowledgements

The author is grateful to David Rydh for valuable comments.

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  1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Andrew Kresch

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  1. Andrew Kresch
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Correspondence to Andrew Kresch.

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Kresch, A. Descent of vector bundles under wildly ramified extensions. European Journal of Mathematics 6, 1255–1263 (2020). https://doi.org/10.1007/s40879-019-00394-9

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