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Which algebraic groups are Picard varieties?

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Abstract

We show that every connected commutative algebraic group over an algebraically closed field of characteristic 0 is the Picard variety of some projective variety having only finitely many non-normal points. In contrast, no Witt group of dimension at least 3 over a perfect field of prime characteristic is isogenous to a Picard variety obtained by this construction.

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  1. Institut Fourier, Université de Grenoble, Saint-Martin d’Hères Cedex, 38402, France

    Michel Brion

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  1. Michel Brion
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Correspondence to Michel Brion.

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Brion, M. Which algebraic groups are Picard varieties?. Sci. China Math. 58, 461–478 (2015). https://doi.org/10.1007/s11425-014-4882-3

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  • DOI: https://doi.org/10.1007/s11425-014-4882-3

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