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Geometric T-Dualization

In this article we realize T-duality as a geometric transform of bundles of abelian group stacks. The transform applies in the algebro-geometric setting as well as the topological setting, and thus makes precise the link between the models of T-duality in these two settings, which are superficially quite different. The transform is also valid for torus bundles with affine structure group, and thus provides a constructive method of producing T-duals in the affine case.