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Which algebraic groups are Picard varieties?

We show that every connected commutative algebraic group over an algebraically closed field of characteristic 0 is the Picard variety of some projective variety, obtained by pinching a smooth variety along a finite subscheme. In contrast, no Witt group of dimension at least 3 over a perfect field of prime characteristic is isogenous to the Picard variety obtained by this construction.

preprint2013arXivOpen access
Michel Brion
math.AG
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Michel Brion

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