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On the Galois structure of equivariant line bundles on curves
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 120, Number 6, December 1998
- pp. 1121-1163
- 10.1353/ajm.1998.0045
- Article
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Let k be a finite field, and let X be a smooth, projective curve over k with structure sheaf [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]. Let G be a finite group, and write C1([inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /][G]) for the reduced Grothendieck group of the category of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /][G]-vector bundles. In this paper we describe explicitly the subgroup of C1([inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /][G]) which is generated by the classes arising from G-stable invertible sheaves on tame Galois covers of X which have Galois group G.