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arXiv · 1409.3616

Intersection Multiplicity of Serre in the Unramified Case

Chris Skalit
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Abstract

We describe here some recent progress pertaining to the Serre Intersection Multiplicity Conjecture. In particular, we show that if A is an unramified regular local ring, then just as in the equicharacteristic case, the intersection multiplicity of two complimentary-dimensional modules is bounded below by the product of their Hilbert-Samuel multiplicities. We also explain, in terms of the blowup of Spec(A) at the closed point, the geometric significance of achieving this lower bound.

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Chris Skalit. 2014-09-11. Intersection Multiplicity of Serre in the Unramified Case. https://arxiv.org/abs/1409.3616

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