| The sign conjecture is a weakening of the K\"unneth standard conjecture; it predicts that there exists motives representing the even and odd parts of the cohomology of a smooth proper variety. I will explain this conjecture and some of its consequences, and then show how, for Shimura varieties, it can be deduced from Arthur's conjectures and the work of Adams-Johnson and Vogan-Zuckerman on cohomological representations. This is joint work with Junecue Suh. |