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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.

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