The standard sign conjecture on algebraic cycles: the case of Shimura   varieties
  We show how to deduce the standard sign conjecture (a weakening of the K\"unneth 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. 
Sophie Morel and Junecue Suh
math.AG math.NT