Cubic structures and ideal class groups |
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Authors: | Georgios Pappas |
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Affiliation: | School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA |
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Abstract: | We establish a generalization of Breen's theory of cubic structures on line bundles over group schemes. We study such “n-cubic structures” inductively using multiextensions. As a result we obtain information on the set of isomorphism classes of line bundles with n-cubic structures over finite multiplicative group schemes over Spec(Z) by relating this set to certain corresponding eigenspaces of ideal class groups of cyclotomic fields. |
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