# Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety

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Joseph Ayoub, University of Zurich
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)