This paper provides a new construction of a supply of Darmon-like points on elliptic curves E defined over a quadratic extension of totally real number fields.

Under mild assumptions, we prove the Iwasawa main conjecture for a cuspidal eigenform at a good prime p.

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Let p be a prime and L be a finite extension of ℚp. We study the ordinary parts of GL2(L)-representations arised in the mod p cohomology of Shimura curves attached to indefinite division algebras which splits at a finite place above p. The main tool of the proof is a theorem of Emerton \cite{Em3}.

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