Picard group of the forms of the affine line and of the additive group

Groupe de Picard des formes de la droite affine et du groupe additif

Raphaël Achet (1)

1 IF - Institut Fourier

We obtain an explicit upper bound on the torsion of the Picard group of the forms of the affine line and their regular completions. We also obtain a sufficient condition for the Picard group of the forms of the affine line to be non trivial and we give examples of non trivial forms of the affine line with trivial Picard groups.

Mots clés: Picard functor; Picard group; Jacobian; Unipotent group; imperfect field; Torsor

Domaines: Géométrie algébrique [math.AG]; Théorie des groupes [math.GR]

Raphaël Achet. Picard group of the forms of the affine line and of the additive group. Journal of Pure and Applied Algebra, 2017, 221 (11), pp.2838-2860. ⟨10.1016/j.jpaa.2017.02.003⟩. ⟨hal-01377384v2⟩