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arXiv · 2004.12172

Local Constancy of Intersection Numbers

Andreas Mihatsch
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Abstract

We prove that, in certain situations, intersection numbers on formal schemes that come in profinite families vary locally constantly in the parameter. To this end, we define the product $S\times M$ of a profinite set $S$ with a locally noetherian formal scheme $M$ and study intersections thereon. Our application is to the Arithmetic Fundamental Lemma of W. Zhang where the result helps to remove a restriction in its recent proof, cf. arXiv:1909.02697.

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Andreas Mihatsch. 2020-04-25. Local Constancy of Intersection Numbers. https://doi.org/10.2140/ant.2022.16.505

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