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Modul:   MAT770  Oberseminar: Algebraische Geometrie


On the irregular case of the Langlands correspondence

Prof. Dr. Wushi Goldring's talk

Date: 20.04.15   Time: 13.15 - 14.45   Room: Y27H25

The Langlands correspondence, coupled with other fundamental conjectures such as that of Fontaine-Mazur, predicts a "basic triangle" of correspondences between (1) certain automorphic representations, (2) certain Galois representations and (3) pure motives. We shall begin by briefly saying something about these three classes of objects and how they are expected to correspond to one another. We will introduce and motivate the regular/irregular dichotomy for the objects (1)-(3), explaining why the irregular case is at the same time more interesting and more difficult. The remainder of the talk will focus on the arrow (1)-->(2) in the irregular case. There are essentially two known techniques for attacking the latter problem: Exploiting the geometry of Shimura varieties and Langlands' Functoriality Principle. We will present recent results and work in progress using each of the two techniques. Our geometric results are joint work with J.-S. Koskivirta, following earlier joint work with M.-H. Nicole.