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Award ID contains: 2001293

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  1. ; (, Forum of Mathematics, Pi)
    We prove that the Jacquet–Langlands correspondence for cohomological automorphic forms on quaternionic Shimura varieties is realized by a Hodge class. Conditional on Kottwitz’s conjecture for Shimura varieties attached to unitary similitude groups, we also show that the image of this Hodge class in ℓ-adic cohomology is Galois invariant for all ℓ. 
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  2. (, International Mathematics Research Notices)
    Abstract We propose an action of a certain motivic cohomology group on the coherent cohomology of Hilbert modular varieties, extending conjectures of Venkatesh, Prasanna, and Harris. The action is described in two ways: on cohomology modulo $$p$$ and over $${\mathbb {C}}$$, and we conjecture that they both lift to an action on cohomology with integral coefficients. The conjecture is supported by theoretical evidence based on Stark’s conjecture on special values of Artin $$L$$-functions and by numerical evidence in base change cases. 
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  3. ; (, Asterisque)
    We propose a relationship between the cohomology of arithmetic groups, and the motivic cohomology of certain (Langlands-)attached motives. The motivic cohomology group in question is that related, by Beilinson’s conjecture, to the adjoint L-function at s=1. We present evidence for the conjecture using the theory of periods of automorphic forms, and using analytic torsion. 
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  4. ; ; ; (, Mathematische Zeitschrift)
    null (Ed.)
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