# Simple description of a Grothendieck topology on the opposite of f.p. complex algebras

Let $${\cal A}$$ be the category of finitely presented $$\mathbb{C}$$-algebras. Let $$J$$ be the largest subcanonical Grothendieck topology on $${{\cal A}^{op}}$$ such that the local algebras in $$\cal A$$ are cocovered only by the maximal sieve. Is there a more explicit description of $$J$$? (Something analogous to the usual description of the Zariski topology in terms of a finitary basis.) Note: it contains the Zariski topology.