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doc(algebraic_geometry/structure_sheaf): fix latex (#6262)
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robertylewis committed Feb 16, 2021
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12 changes: 6 additions & 6 deletions src/algebraic_geometry/structure_sheaf.lean
Expand Up @@ -89,12 +89,12 @@ consisting of those functions which can locally be expressed as a ratio of
Quoting Hartshorne:
For an open set $$U ⊆ Spec A$$, we define $$𝒪(U)$$ to be the set of functions
$$s : U → ⨆_{𝔭 ∈ U} A_𝔭$$, such that $s(𝔭) ∈ A_𝔭$$ for each $$𝔭$$,
and such that $$s$$ is locally a quotient of elements of $$A$$:
to be precise, we require that for each $$𝔭 ∈ U$$, there is a neighborhood $$V$$ of $$𝔭$$,
contained in $$U$$, and elements $$a, f ∈ A$$, such that for each $$𝔮 ∈ V, f ∉ 𝔮$$,
and $$s(𝔮) = a/f$$ in $$A_𝔮$$.
For an open set $U ⊆ Spec A$, we define $𝒪(U)$ to be the set of functions
$s : U → ⨆_{𝔭 ∈ U} A_𝔭$, such that $s(𝔭) ∈ A_𝔭$ for each $𝔭$,
and such that $s$ is locally a quotient of elements of $A$:
to be precise, we require that for each $𝔭 ∈ U$, there is a neighborhood $V$ of $𝔭$,
contained in $U$, and elements $a, f ∈ A$, such that for each $𝔮 ∈ V, f ∉ 𝔮$,
and $s(𝔮) = a/f$ in $A_𝔮$.
Now Hartshorne had the disadvantage of not knowing about dependent functions,
so we replace his circumlocution about functions into a disjoint union with
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