Towards a Proof of the Conjecture of Langlands and Rapoport
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Points on Shimura varieties over finite fields: the conjecture of Langlands and Rapoport
The purpose of this article is to state a strong form of the conjecture of Langlands and Rapoport (1987, §5), and to outline a proof of it. For Shimura varieties of PEL type, the outline is complete, and for Shimura varieties of Hodge type it becomes complete if one accepts certain statements, stated as conjectures in the original version of this article, whose proof has been announced by Vasiu...
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FORENOTE (2007): The remarkable conjecture of Langlands and Rapoport (1987) gives a purely group-theoretic description of the points on a Shimura variety modulo a prime of good reduction. In an article in the proceedings of the 1991 Motives conference (Milne 1994, §4), I gave a heuristic derivation of the conjecture assuming a sufficiently good theory of motives in mixed characteristic. I wrote...
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We explain, in the case of good reduction, the conjecture of Langlands and Rapoport describing the structure of the points on the reduction of a Shimura variety (Langlands and Rapoport 1987, 5.e, p169), and we derive from it the formula conjectured in (Kottwitz 1990, 3.1), which expresses a certain trace as a sum of products of (twisted) orbital integrals. Also we introduce the notion of an int...
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The conjecture of Langlands and Rapoport provides a precise description of the points on a Shimura variety modulo a prime of good reduction. We reene 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 reened conjecture for a Shimura variety depends only on the asso...
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In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...
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تاریخ انتشار 2000