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arXiv · 1803.07553

An intersection number formula for CM cycles in Lubin-Tate towers

Qirui Li
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Abstract

We give an explicit formula for the arithmetic intersection number of CM cycles on Lubin-Tate spaces for all levels. We prove our formula by formulating the intersection number on the infinite level. Our CM cycles are constructed by choosing two separable quadratic extensions $K_1,K_2/F$ of non-Archimedean local fields $F$. Our formula works for all cases, $K_1$ and $K_2$ can be either the same or different, ramify or unramified. As applications, this formula translate the linear Arithmetic Fundamental Lemma (linear AFL) into a comparison of integrals. This formula can also be used to recover Gross and Keating's result on lifting endomorphism of formal modules.

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Qirui Li. 2018-03-20. An intersection number formula for CM cycles in Lubin-Tate towers. https://arxiv.org/abs/1803.07553

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