Geodesic
On the intersection multiplicity of images under an etale morphism
Colloquium Mathematicum, Tome 75 (1998) no. 2, pp. 167-174.

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We present a formula for the intersection multiplicity of the images of two subvarieties under an etale morphism between smooth varieties over a field k. It is a generalization of Fulton's Example 8.2.5 from [3], where a strong additional assumption has been imposed. In a special case where the base field k is algebraically closed and a proper component of the intersection is a closed point, intersection multiplicity is an invariant of etale morphisms. This corresponds with analytic geometry where intersection multiplicity is an invariant of local biholomorphisms.
DOI : 10.4064/cm-75-2-167-174
Keywords: intersection multiplicity, multiplicity of ideals in a semilocal ring, etale morphisms, unramified morphisms, algebraic varieties

Krzysztof Nowak 1

1 
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Krzysztof Nowak. On the intersection multiplicity of images under an etale morphism. Colloquium Mathematicum, Tome 75 (1998) no. 2, pp. 167-174. doi : 10.4064/cm-75-2-167-174. http://geodesic.mathdoc.fr/articles/10.4064/cm-75-2-167-174/

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