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The standard sign conjecture on algebraic cycles: The case of Shimura varieties

Sophie Morel and Junecue Suh

Abstract

We show how to deduce the standard sign conjecture (a weakening of the Künneth standard conjecture) for Shimura varieties from some statements about discrete automorphic representations (Arthur’s conjectures plus a bit more). We also indicate what is known (to us) about these statements.

Acknowledgements

We thank Pierre Deligne for helpful discussions, especially regarding the material on finite correspondences in the final section. We also thank Colette Moeglin for pointing out some misconceptions about Arthur’s conjectures in a previous version of this article.

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Received: 2014-09-17
Revised: 2016-07-26
Published Online: 2016-09-01
Published in Print: 2019-03-01

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