On the Galois structure of equivariant line bundles on curves
A. Agboola, D. Burns
Source abstract
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 .
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