Displaying similar documents to “On non-commutative twisting in étale and motivic cohomology”

Second cohomology classes of the group of C 1 -flat diffeomorphisms

Tomohiko Ishida (2012)

Annales de l’institut Fourier

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We study the cohomology of the group consisting of all C ∞ -diffeomorphisms of the line, which are C 1 -flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.

Hida families, p -adic heights, and derivatives

Trevor Arnold (2010)

Annales de l’institut Fourier

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This paper concerns the arithmetic of certain p -adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a p -adic regulator, and the derivative of a p -adic L -function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions,...

Vanishing of the first reduced cohomology with values in an L p -representation

Romain Tessera (2009)

Annales de l’institut Fourier

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We prove that the first reduced cohomology with values in a mixing L p -representation, 1 < p < ∞ , vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced ℓ p -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced L p -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes....