We relate the p-adic heights of generalized Heegner cycles to the derivative of a p-adic L-function attached to a pair (f, χ), where f is an ordinary weight 2r newform and χ is an unramified imaginary quadratic Hecke character of infinity type (ℓ, 0), with 0 < ℓ < 2r. This generalizes the p-adic Gross-Zagier formula in the case ℓ = 0 due to Perrin-Riou (in weight two) and Nekovář (in higher weight).
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I am grateful to Kartik Prasanna for suggesting this problem and for his patience and direction. Thanks go to Hunter Brooks for several productive conversations. I also thank Bhargav Bhatt, Daniel Disegni, Yara Elias, Olivier Fouquet, Adrian Iovita, Shinichi Kobayashi, Jan Nekovář, and Martin Olsson for helpful correspondence. The author was partially supported by National Science Foundation RTG grant DMS-0943832.
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- Algebraic cycles
- Modular forms
- p-adic L-functions