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$$p$$-adic families of modular forms and $$p$$-adic Abel-Jacobi maps. (English. French summary) Zbl 1417.11101
Summary: We show that $$p$$-adic families of modular forms give rise to certain $$p$$-adic Abel-Jacobi maps at their $$p$$-new specializations. We introduce the concept of differentiation of distributions, using it to give a new description of the Coleman-Teitelbaum cocycle that arises in the context of the $$\mathcal {L}$$-invariant.

##### MSC:
 11F85 $$p$$-adic theory, local fields 11F41 Automorphic forms on $$\mbox{GL}(2)$$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
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