The conjecture of Langlands and Rapoport for Siegel modular varieties

The Conjecture of Langlands and Rapoport for Siegel Modular Varieties

Frequently one attaches to an arithmetic object a zeta function whose analytic behavior reflects deep properties of the object. For example, attached to Q there is the Riemann zeta function, whose behavior (especially the position of its zeros) contains information about the distribution of the prime numbers. Dedekind attached a zeta function to every algebraic number field, and Hasse and Weil ...

On the Conjecture of Langlands and Rapoport

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...

The Conjecture of Langlands and Rapoport for Certain Shimura Varieties of Non-rational Weight

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...

Towards a Proof of the Conjecture of Langlands and Rapoport

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...