At the end of the following document, https://public.websites.umich.edu/~asnowden/seminar/2014/gz/L07.pdf , it was stated that to prove the formula of Gross and Zagier, it is not necessary to compute the "local height symbol" when the support overlap due to a trick of Nekovar. However, Snowden did not explain this further nor did he provide a reference. Does anyone know what he is referring to? Thanks in advance for any help.
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The reference is his 1995 Math Annalen paper "On the $p$-adic height of Heegner cycles". See e.g. the discussion on page 6.
The fact that the $q$-expansion of height pairings is modular is also used in the proof of the Yuan-Zhang-Zhang formula, for the same reason (to avoid local heights with improper intersection).
