Which algebraic groups are Picard varieties?

Michel Brion (1)

1 IF - Institut Fourier

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.

Domaines: Géométrie algébrique [math.AG]

Michel Brion. Which algebraic groups are Picard varieties?. Science China Mathematics, 2015, 58 (3), pp.461-478. ⟨10.1007/s11425-014-4882-3⟩. ⟨hal-01622785⟩