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)