In algebraic geometry, a Noetherian local ring R is called parafactorial if it has depth at least 2 and the Picard group Pic(Spec(R) − m) of its spectrum with the closed point m removed is trivial.

More generally, a scheme X is called parafactorial along a closed subset Z if the subset Z is "too small" for invertible sheaves to detect; more precisely if for every open set V the map from P(V) to P(V ∩ U) is an equivalence of categories, where U = X – Z and P(V) is the category of invertible sheaves on V. A Noetherian local ring is parafactorial if and only if its spectrum is parafactorial along its closed point.

Parafactorial local rings were introduced by Grothendieck (1967, 21.13, 1968, XI 3.1,3.2)