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Descent of vector bundles under wildly ramified extensions


Kresch, Andrew (2020). Descent of vector bundles under wildly ramified extensions. European Journal of Mathematics:Epub ahead of print.

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.

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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Additional indexing

Item Type:Journal Article, not_refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Uncontrolled Keywords:General Mathematics
Language:English
Date:2 January 2020
Deposited On:09 Jan 2020 12:14
Last Modified:07 Apr 2020 07:24
Publisher:Springer
ISSN:2199-675X
OA Status:Closed
Publisher DOI:https://doi.org/10.1007/s40879-019-00394-9

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