# On the intersection multiplicity of images under an etale morphism

Colloquium Mathematicae (1998)

- Volume: 75, Issue: 2, page 167-174
- ISSN: 0010-1354

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topNowak, Krzysztof. "On the intersection multiplicity of images under an etale morphism." Colloquium Mathematicae 75.2 (1998): 167-174. <http://eudml.org/doc/210535>.

@article{Nowak1998,

abstract = {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.},

author = {Nowak, Krzysztof},

journal = {Colloquium Mathematicae},

keywords = {intersection multiplicity; multiplicity of ideals in a semilocal ring; etale morphisms; unramified morphisms; algebraic varieties; étale morphism},

language = {eng},

number = {2},

pages = {167-174},

title = {On the intersection multiplicity of images under an etale morphism},

url = {http://eudml.org/doc/210535},

volume = {75},

year = {1998},

}

TY - JOUR

AU - Nowak, Krzysztof

TI - On the intersection multiplicity of images under an etale morphism

JO - Colloquium Mathematicae

PY - 1998

VL - 75

IS - 2

SP - 167

EP - 174

AB - 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.

LA - eng

KW - intersection multiplicity; multiplicity of ideals in a semilocal ring; etale morphisms; unramified morphisms; algebraic varieties; étale morphism

UR - http://eudml.org/doc/210535

ER -

## References

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- [9] K. J. Nowak, A proof of the criterion for multiplicity one, ibid., 247-250.
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