Tamely ramified Hida theory

Assaf Goldberger; Ehud de Shalit

Displaying similar documents to “Tamely ramified Hida theory”

On certain Galois representations related to the modular curve $X_{1} (p)$

Ehud De Shalit (1995)

Compositio Mathematica

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On component groups of Jacobians of Drinfeld modular curves

Mihran Papikian (2004)

Annales de l'Institut Fourier

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Let $J_{0} (𝔫)$ be the Jacobian variety of the Drinfeld modular curve $X_{0} (𝔫)$ over $𝔽_{q} (t)$ , where $𝔫$ is an ideal in $𝔽_{q} [t]$ . Let $0 \to B \to J_{0} (𝔫) \to A \to 0$ be an exact sequence of abelian varieties. Assume $B$ , as a subvariety of $J_{0} (𝔫)$ , is stable under the action of the Hecke algebra $𝕋 \subset$ End $(J_{0} (𝔫))$ . We give a criterion which is sufficient for the exactness of the induced sequence of component groups $0 \to Φ_{B, \infty} \to Φ_{J, \infty} \to Φ_{A, \infty} \to 0$ of the Néron models of these abelian varieties over $𝔽_{q} [[\frac{1}{t}]]$ . This criterion is always satisfied when either $A$ or $B$ is one-dimensional. Moreover, we prove that...

Modular curves and the Eisenstein ideal

Barry Mazur (1977)

Publications Mathématiques de l'IHÉS

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On $p$ -adic analytic families of Galois representations

B. Mazur, A. Wiles (1986)

Compositio Mathematica

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On the torsion of the Mordell-Weil group of the Jacobian of Drinfeld modular curves.

Pál, Ambrus (2005)

Documenta Mathematica

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Endomorphism algebras of motives attached to elliptic modular forms

Alexander F. Brown, Eknath P. Ghate (2003)

Annales de l’institut Fourier

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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...

Displaying similar documents to “Tamely ramified Hida theory”

On certain Galois representations related to the modular curve X 1 ( p )

On component groups of Jacobians of Drinfeld modular curves

Modular curves and the Eisenstein ideal

On p -adic analytic families of Galois representations

On the torsion of the Mordell-Weil group of the Jacobian of Drinfeld modular curves.

Endomorphism algebras of motives attached to elliptic modular forms

On certain Galois representations related to the modular curve $X_{1} (p)$

On $p$ -adic analytic families of Galois representations