The p-adic Gross-Zagier formula describes the derivative of the p-adic L-function in terms of the p-adic height of Heegner cycle (Heegner point if the weight is two). Together with the classical Gross-Zagier formula, it has a striking application for the full Birch and Swinnerton-Dyer conjecture.
The formula was proved by B. Perrin-Riou (weight 2) and by J. Nekovar (higher weight) at good ordinary primes, and by the lecturer at non-ordinary primes. In this course, I explain the proof with a special emphasis on the non-ordinary case. (However, the proof also works (includes) the ordinary case.)

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