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 K1, K2/F of non-Archimedean local fields F . Our formula works for all cases, K1 and K2 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.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/D8KS880K |
| Date | January 2018 |
| Creators | Li, Qirui |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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