Modular curves and unramified extensions of number fields

S. Kamienny

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Displaying similar documents to “Modular curves and unramified extensions of number fields”

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We study the endomorphism algebra of the motive attached to a non-CM elliptic modular cusp form. We prove that this algebra has a sub-algebra isomorphic to a certain crossed product algebra $X$ . The Tate conjecture predicts that $X$ is the full endomorphism algebra of the motive. We also investigate the Brauer class of $X$ . For example we show that if the nebentypus is real and $p$ is a prime that does not divide the level, then the local behaviour of $X$ at a place lying above $p$ is essentially...

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