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  THE CONJECTURE OF LANGLANDS AND RAPOPORT FOR CERTAIN SHIMURA VARIETIES OF NON-RATIONAL WEIGHT

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by Matthias Pfau
http://www.mathematik.uni-bielefeld.de/sfb343/preprints/pr94069.ps.gz
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Abstract:

Abstract. The conjecture of Langlands and Rapoport provides a precise description of the points on a Shimura variety modulo a prime of good reduction. We refine the conjecture so that it also describes the points on the reduction of each connected component of the Shimura variety, and we prove (under some hypotheses) that the validity of the refined conjecture for a Shimura variety depends only on the associated connected variety. Using that the conjecture is known for Shimura varieties of PELtype, we deduce the conjecture for other Shimura varieties, including some whose weight is not defined over Q.

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