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

被引：14
|
作者：
Goertz, Ulrich
Haines, Thomas J.
机构：
[1] Univ Bonn, Inst Math, D-53115 Bonn, Germany
[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA
来源：
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2007年 / 609卷
基金：
美国国家科学基金会;
关键词：
D O I：
10.1515/CRELLE.2007.063
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the Jordan-Hoder 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.
引用
收藏
页码：161 / 213
页数：53
相关论文
共 50 条
  • [1] Nearby cycles for local models of some Shimura varieties
    Haines, T
    Ngô, BC
    COMPOSITIO MATHEMATICA, 2002, 133 (02) : 117 - 150
  • [2] HIGHER NEARBY CYCLES AND CENTRAL SHEAVES ON AFFINE FLAG VARIETIES
    Achar, Pramod n.
    Riche, Simon
    JOURNAL OF SINGULARITIES, 2024, 27 : 1 - 30
  • [3] ON JORDAN-HOLDER SERIES OF SOME LOCALLY ANALYTIC REPRESENTATIONS
    Orlik, Sascha
    Strauch, Matthias
    JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 28 (01) : 99 - 157
  • [4] Kottwitz’s nearby cycles conjecture for a class of unitary Shimura varieties
    Sean Rostami
    Selecta Mathematica, 2017, 23 : 643 - 719
  • [5] Kottwitz's nearby cycles conjecture for a class of unitary Shimura varieties
    Rostami, Sean
    SELECTA MATHEMATICA-NEW SERIES, 2017, 23 (01): : 643 - 719
  • [6] Tate cycles on some unitary Shimura varieties mod
    Helm, David
    Tian, Yichao
    Xiao, Liang
    ALGEBRA & NUMBER THEORY, 2017, 11 (10) : 2213 - 2288
  • [7] Affine Deligne-Lusztig varieties in affine flag varieties
    Goertz, Ulrich
    Haines, Thomas J.
    Kottwitz, Robert E.
    Reuman, Daniel C.
    COMPOSITIO MATHEMATICA, 2010, 146 (05) : 1339 - 1382
  • [8] Remarks on generating series for special cycles on orthogonal Shimura varieties
    Kudla, Stephen S.
    ALGEBRA & NUMBER THEORY, 2021, 15 (10) : 2403 - 2447
  • [9] Combinatorics in affine flag varieties
    Parkinson, James
    Ram, Arun
    Schwer, Christoph
    JOURNAL OF ALGEBRA, 2009, 321 (11) : 3469 - 3493
  • [10] DIMENSIONS OF AFFINE DELIGNE-LUSZTIG VARIETIES IN AFFINE FLAG VARIETIES
    Goertz, Ulrich
    He, Xuhua
    DOCUMENTA MATHEMATICA, 2010, 15 : 1009 - 1028
12345