Heegner points, p-adic L-functions, and the Cerednik-Drinfeld uniformization

1 Quaternion algebras, upper half planes, and trees . . . . . . . . . . . . 4 2 The p-adic L-function . . . . . . . . . . . . . . . . . . . . . . . 11 3 Generalities on Mumford curves . . . . . . . . . . . . . . . . . . . 17 4 Shimura curves . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5 Heegner points . . . . . . . . . . . . . . . . . . . . . . . . . . 28 6 Computing the p-adic Abel-Jacobi map . . . . . . . . . . . . . . . 29 7 Proof of the main results . . . . . . . . . . . . . . . . . . . . . 34

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