Dirichlet motives via modular curves

Annette Huber; Guido Kings

Displaying similar documents to “Dirichlet motives via modular curves”

On the Fourier coefficients of modular forms

Douglas L. Ulmer (1995)

Annales scientifiques de l'École Normale Supérieure

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Boundary cohomology of Shimura varieties. I. Coherent cohomology on toroidal compactifications

Michael Harris, Steven Zucker (1994)

Annales scientifiques de l'École Normale Supérieure

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Galois representations modulo p and cohomology of Hilbert modular varieties

Mladen Dimitrov (2005)

Annales scientifiques de l'École Normale Supérieure

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On non-commutative twisting in étale and motivic cohomology

Jens Hornbostel, Guido Kings (2006)

Annales de l’institut Fourier

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This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups $H^{1} (𝒪_{K} [1 / S], H^{i} (\bar{X}, ℚ_{p} (j)))$ , where $X \to Spec 𝒪_{K} [1 / S]$ is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to $H^{i} (\bar{X}, ℤ_{p} (j))$ . Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.

Weights in cohomology and the Eilenberg-Moore spectral sequence

Matthias Franz, Andrzej Weber (2005)

Annales de l’institut Fourier

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We show that in the category of complex algebraic varieties, the Eilenberg–Moore spectral sequence can be endowed with a weight filtration. This implies that it degenerates if all spaces involved have pure cohomology. As application, we compute the rational cohomology of an algebraic $G$ -variety $X$ ( $G$ being a connected algebraic group) in terms of its equivariant cohomology provided that $H_{G}^{*} (X)$ is pure. This is the case, for example, if $X$ is smooth and has only finitely many orbits. We work...