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arXiv · 1408.4039

Twisted forms of toric varieties

Alexander Duncan
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Abstract

We consider the set of forms of a toric variety over an arbitrary field: those varieties which become isomorphic to a toric variety after base field extension. In contrast to most previous work, we also consider arbitrary isomorphisms rather than just those that respect a torus action. We define an injective map from the set of forms of a toric variety to a non-abelian second cohomology set, which generalizes the usual Brauer class of a Severi-Brauer variety. Additionally, we define a map from the set of forms of a toric variety to the set of forms of a separable algebra along similar lines to a construction of A. Merkurjev and I. Panin. This generalizes both a result of M.~Blunk for del Pezzo surfaces of degree 6, and the standard bijection between Severi-Brauer varieties and central simple algebras

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Alexander Duncan. 2016-01-19. Twisted forms of toric varieties. https://doi.org/10.1007/s00031-016-9394-5

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