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-invariants and Darmon cycles attached to modular forms

Victor RotgerMarco Adamo Seveso — 2012

Journal of the European Mathematical Society

Let f be a modular eigenform of even weight k 2 and new at a prime p dividing exactly the level with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to f a monodromy module D f F M and an -invariant f F M . The first goal of this paper is building a suitable p -adic integration theory that allows us to construct a new monodromy module D f and -invariant f , in the spirit of Darmon. The two monodromy modules are isomorphic, and in particular the two -invariants are equal....

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