Abstract
Let (A, θ) be a principally polarized abelian threefold over a perfect field k, not isomorphic to a product over \({\bar k}\) . There exists a canonical extension k′/k, of degree ≤ 2, such that (A, θ) becomes isomorphic to a Jacobian over k′. The aim of this note is to give a geometric construction of this extension.
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Beauville, A., Ritzenthaler, C. Jacobians among abelian threefolds: a geometric approach. Math. Ann. 350, 793–799 (2011). https://doi.org/10.1007/s00208-010-0583-6
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DOI: https://doi.org/10.1007/s00208-010-0583-6