The Jordan-Hoelder series for nearby cycles on some Shimura varieties and affine flag varieties

Details The Jordan-Hoelder series for nearby cycles on some Shimura varieties and affine flag varieties The Jordan-Hoelder series for nearby cycles on some Shimura varieties and affine flag varieties

2004-02-09

arxiv.org/abs/math/0402143v1

Mathematics

Algebraic Geometry

71 pp

Scientific paper

We study the Jordan-Hoelder series for nearby cycles on certain Shimura varieties and Rapoport-Zink local models, and on finite-dimensional pieces of Beilinson's deformation of the affine Grassmannian to the affine flag variety (and their p-adic analogues). We give a formula for the multiplicities of irreducible constituents in terms of certain cohomology groups, and we also provide an algorithm to compute multiplicities, in terms of the affine Hecke algebra.

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