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)