An introduction to motives

An introduction to motives

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Joseph Ayoub, University of Zurich
Fine Hall 322

PLEASE NOTE SPECIAL TIME AND LOCATION. This is in addition to the regular PU/IAS Number Theory Seminar.  We review the construction of the triangulated categories of motives over a base scheme (following the method of Morel and Voevodsky). We then explain quickly the construction of various operations between these categories as well as some realization functors (Betti and $\ell$-adic). If time permits, we also discuss the rigid analytic variant and develop an application to the theory of nearby and vanishing cycles.