Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The p-adic Gross-Zagier formula on Shimura curves   We prove a general formula for the $p$-adic heights of Heegner points on
modular abelian varieties with potentially ordinary (good or semistable)
reduction at the primes above $p$. The formula is in terms of the cyclotomic
derivative of a Rankin-Selberg $p$-adic $L$-function, which we construct. It
generalises previous work of Perrin-Riou, Howard, and the author, to the
context of the work of Yuan-Zhang-Zhang on the archimedean Gross-Zagier formula
and of Waldspurger on toric periods. We further construct analytic functions
interpolating Heegner points in the anticyclotomic variables, and obtain a
version of our formula for them. It is complemented, when the relevant root
number is $+1$ rather than $-1$, by an anticyclotomic version of the
Waldspurger formula. When combined with work of Fouquet, the anticyclotomic
Gross-Zagier formula implies one divisibility in a $p$-adic Birch and
Swinnerton-Dyer conjecture in anticyclotomic families. Other applications
described in the text will appear separately.

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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph