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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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