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secondary 16b50

Proceedings of the Edinburgh Mathematical Society (1)

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THE GROUP OF COVERING AUTOMORPHISMS OF A QUASI-COHERENT SHEAF ON $\bm{P}^1(K)$
E. Enochs, S. Estrada, J. R. García Rozas, L. Oyonarte
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 2 / June 2007

Published online by Cambridge University Press:

17 May 2007, pp. 325-341
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CoGalois groups appear in a natural way in the study of covers. They generalize the well-known group of covering automorphisms associated with universal covering spaces. Recently, it has been proved that each quasi-coherent sheaf over the projective line $\bm{P}^1(R)$ ($R$ is a commutative ring) admits a flat cover and so we have the associated coGalois group of the cover. In general the problem of computing coGalois groups is difficult. We study a wide class of quasi-coherent sheaves whose associated coGalois groups admit a very accurate description in terms of topological properties. This class includes finitely generated and cogenerated sheaves and therefore, in particular, vector bundles.