# Relative Artin Motives and the Reductive Borel-Serre Compactification of a Locally Symmetric Variety

 Joint IAS/PU Number Theory Seminar Topic: Relative Artin Motives and the Reductive Borel-Serre Compactification of a Locally Symmetric Variety Speaker: Joseph Ayoub Affiliation: University of Zurich Date: Thursday, February 7 Time/Room: 4:30pm - 5:30pm/Fine Hall 214

Let $X$ be a locally symmetric variety, $\bar{X}$ its Baily-Borel compactification, $\bar{X}^{rbs}$ its reductive Borel-Serre compactification and $p:\bar{X}^{rbs} \to \bar{X}$ the canonical map. We prove that the derived direct image sheaf $Rp_*\mathbb{Q}$ is the realization of a canonical motive associated to the variety $\bar{X}$. This is non trivial since $\bar{X}^{rbs}$ is not an algebraic variety in general. (Joint with S. Zucker)