English

Which algebraic groups are Picard varieties?

Algebraic Geometry 2013-12-24 v2

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, 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.

Keywords

Cite

@article{arxiv.1310.0186,
  title  = {Which algebraic groups are Picard varieties?},
  author = {Michel Brion},
  journal= {arXiv preprint arXiv:1310.0186},
  year   = {2013}
}

Comments

Statement and proof of Theorem 2 corrected

R2 v1 2026-06-22T01:37:50.968Z