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Search Results: 1 - 10 of 401597 matches for " M. Rapoport "
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A guide to the reduction modulo p of Shimura varieties
M. Rapoport
Mathematics , 2002,
Abstract: This is a report on results and methods in the reduction modulo p of Shimura varieties with parahoric level structure. In the first part, the local theory, we explain the concepts of parahoric subgroups, of the mu-admissible and mu-permissible subsets of the Iwahori-Weyl group, of the corresponding union of affine Deligne-Lusztig varieties and of local models. In the second part, the global theory, we use these concepts to formulate conjectures on the points in the reduction modulo p of Shimura varieties with parahoric level structure.
Deligne-Lusztig varieties and period domains over finite fields
S. Orlik,M. Rapoport
Mathematics , 2007,
Abstract: We prove that the Drinfeld halfspace is essentially the only Deligne-Lusztig variety which is at the same time a period domain over a finite field. This is done by comparing a cohomology vanishing theorem for DL-varieties, due to Digne, Michel, and Rouquier, with a non-vanishing theorem for PD, due to the first author. We also discuss an affineness criterion for DL-varieties.
On parahoric subgroups
T. Haines,M. Rapoport
Mathematics , 2008,
Abstract: We prove some basic facts on parahoric subgroups and on Iwahori-Weyl groups.
Phi-modules and coefficient spaces
G. Pappas,M. Rapoport
Mathematics , 2008,
Abstract: We define and study certain moduli stacks of modules equipped with a Frobenius semi-linear endomorphism. These stacks can be thought of as parametrizing the coefficients of a variable Galois representation and are global variants of the spaces of Kisin-Breuil $\Phi$-modules used by Kisin in his study of deformation spaces of local Galois representations. We also define a version of a rigid analytic period map for these spaces, we show how their local structure can be described in terms of "local models", and we show how Bruhat-Tits buildings can be used to study their special fibers.
On the Drinfeld moduli problem of p-divisible groups
M. Rapoport,Th. Zink
Mathematics , 2014,
Abstract: Let $O_D$ be the ring of integers in a division algebra of invariant $1/n$ over a p-adic local field. Drinfeld proved that the moduli problem of special formal $O_D$-modules is representable by Deligne's formal scheme version of the Drinfeld p-adic halfspace. In this paper we exhibit other moduli spaces of formal $p$-divisible groups which are represented by $p$-adic formal schemes whose generic fibers are isomorphic to the Drinfeld p-adic halfspace. We also prove an analogue concerning the Lubin-Tate moduli space.
Height pairings on Shimura curves and p-adic uniformization
S. Kudla,M. Rapoport
Mathematics , 1998,
Abstract: We establish a relation between intersection numbers of special cycles on a Shimura curve and special values of derivatives of metaplectic Eisenstein series at a place of bad reduction where p-adic uniformization in the sense of Cherednik and Drinfeld holds. The result extends the one established by one of us (S. Kudla: Ann. of Math. 146 (1997)) for the archimedean place and for the non-archimedean places of good reduction. The bulk of the paper is concerned with the corresponding problem on the Drinfeld upper half plane (the formal scheme version).
On the existence of F-crystals
R. Kottwitz,M. Rapoport
Mathematics , 2002,
Abstract: Let (N,F) be an F-isocrystal, with associated Newton vector \nu in (Q^n)_+. To any lattice M in N (an F-crystal) is associated its Hodge vector \mu(M) in (Z^n)_+. By Mazur's inequality we have \mu(M)>= \nu. We show that, conversely, for any \mu in (Z^n)_+ with \mu >= \nu, there exists a lattice M in N such that \mu=\mu(M). We also give variants of this existence theorem for symplectic F-isocrystals, and for periodic lattice chains.
Local Models in the ramified case. III. Unitary groups
G. Pappas,M. Rapoport
Mathematics , 2007,
Abstract: We continue our study of the reduction of PEL Shimura varieties with parahoric level structure at primes p at which the group that defines the Shimura variety ramifies. We describe "good" $p$-adic integral models of these Shimura varieties and study their 'etale local structure. In this paper we mainly concentrate on the case of unitary groups for a ramified quadratic extension. Some of our results are applications of the theory of twisted affine flag varieties in our previous paper math.AG/0607130.
Some questions about $\mathcal G$-bundles on curves
G. Pappas,M. Rapoport
Mathematics , 2008,
Abstract: We define the notion of a parahoric group scheme $\mathcal G$ over a smooth projective curve, and formulate four conjectures on the structure of the stack of $\mathcal G$-bundles, which generalize to this case well-known results on $G$-bundles with $G$ a constant reductive group. The conjectures concern the set of connected components, the uniformization by affine flag varieties of twisted loop groups, the Picard groups, and the space of global sections of a dominant line bundle. Since a first version of this paper was circulated, Heinloth [arXiv:0711.4450] has proved a good part of these conjectures.
Twisted loop groups and their affine flag varieties
G. Pappas,M. Rapoport
Mathematics , 2006,
Abstract: We develop a theory of affine flag varieties and of their Schubert varieties for reductive groups over a Laurent power series local field k((t)) with k a perfect field. This can be viewed as a generalization of the theory of affine flag varieties for loop groups to a "twisted case"; a consequence of our results is that our construction also includes the flag varieties for Kac-Moody Lie algebras of affine type. We also give a coherence conjecture on the dimensions of the spaces of global sections of the natural ample line bundles on the partial flag varieties attached to a fixed group over k((t)) and some applications to local models of Shimura varieties.
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