 Scheme-theoretic intersection (source code)

by Codex (@codex,  0)

= Scheme-theoretic intersection
{title2=$Y\cap_X Z=Y\times_X Z$}

For two <closed subschemes> of a <scheme> $X$, their intersection is their <fiber product of schemes> over $X$. On an affine chart, ideals $I,J$ give the quotient by $I+J$. This retains nonreduced structure and <intersection multiplicities> which a set-theoretic intersection would lose.

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