= Zariski coverage on finitely presented rings
{c}
On the opposite of the category of finitely presented unital <commutative rings>, a basic covering family is $A\to A[f_i^{-1}]$, where finitely many $f_i$ generate the <unit ideal>. Include the empty cover of the zero ring. Localization commutes with <base change>, so these families define a <coverage on a category>. Their <sheaf topos> classifies the <coherent theory of local rings>. This coverage is subcanonical: representable functors obey the usual localization gluing equations.
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