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Geometric Representation Theory
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David Helm, PMA 10.176: The categorical local Langlands correspondence and local-global compatibility
Friday, September 09, 2022, 11:00am - 12:00pm
For a reductive group G over Q, the Langlands correspondence predicts a relationship between (some of the) automorphic representations of the adelic points of G and representations of the absolute Galois group of Q, valued in the Langlands dual group of G. This correspondence (or part of it, at least) is mediated by the cohomology of Shimura varieties. Recently, new perspectives on the local Langlands correspondence, coming from modular representation theory and the geometric Langlands correspondence, give two approaches to a conjectural description of the structure of this cohomology, as an object in a suitable derived category. After explaining the classical approach to these objects we will develop both approaches, and explain the links between the two perspectives.
Location: PMA 10.176

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