Duke Mathematical Journal

Normality and Cohen–Macaulayness of local models of Shimura varieties

Xuhua He

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We prove that in the unramified case, local models of Shimura varieties with Iwahori level structure are normal and Cohen–Macaulay.

Article information

Duke Math. J., Volume 162, Number 13 (2013), 2509-2523.

First available in Project Euclid: 8 October 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
Secondary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 14M27: Compactifications; symmetric and spherical varieties


He, Xuhua. Normality and Cohen–Macaulayness of local models of Shimura varieties. Duke Math. J. 162 (2013), no. 13, 2509--2523. doi:10.1215/00127094-2371864. https://projecteuclid.org/euclid.dmj/1381238851

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  • [1] M. Brion, The behaviour at infinity of the Bruhat decomposition, Comment. Math. Helv. 73 (1998), 137–174.
  • [2] M. Brion and P. Polo, Large Schubert varieties, Represent. Theory 4 (2000), 97–126.
  • [3] R. W. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, Wiley-Interscience, Chichester, 1993.
  • [4] C. De Concini and C. Procesi, “Complete symmetric varieties” in Invariant Theory (Montecatini, 1982), Lecture Notes in Math. 996, Springer, Berlin, 1983, 1–44.
  • [5] G. Faltings, Moduli-stacks for bundles on semistable curves, Math. Ann. 304 (1996), 489–515.
  • [6] G. Faltings, Explicit resolution of local singularities of moduli-spaces, J. Reine Angew. Math. 483 (1997), 183–196.
  • [7] G. Faltings, Algebraic loop groups and moduli spaces of bundles, J. Eur. Math. Soc. (JEMS) 5 (2003), 41–68.
  • [8] U. Görtz, On the flatness of models of certain Shimura varieties of PEL-type, Math. Ann. 321 (2001), 689–727.
  • [9] U. Görtz, On the flatness of local models for the symplectic group, Adv. Math. 176 (2003), 89–115.
  • [10] X. He, Closure of Steinberg fibers and affine Deligne-Lusztig varieties, Int. Math. Res. Not. IMRN 14 (2011), 3237–3260.
  • [11] X. He and T. Lam, Projected Richardson varieties and affine Schubert varieties, preprint, arXiv:1106.2586 [math.AG].
  • [12] X. He and J. F. Thomsen, Geometry of $B\times B$-orbit closures in equivariant embeddings, Adv. Math. 216 (2007), 626–646.
  • [13] X. He and T. Wedhorn, On parahoric reductions of Shimura varieties of PEL type, in preparation.
  • [14] M. Kisin, Moduli of finite flat group schemes, and modularity, Ann. of Math. (2) 170 (2009), 1085–1180.
  • [15] G. Lusztig, Parabolic character sheaves, II, Mosc. Math J. 4 (2004), 869–896, 981.
  • [16] G. Pappas and M. Rapoport, Local models in the ramified case, I: The EL-case, J. Algebraic Geom. 12 (2003), 107–145.
  • [17] G. Pappas and M. Rapoport, Local models in the ramified case, II: Splitting models, Duke Math. J. 127 (2005), 193–250.
  • [18] G. Pappas and M. Rapoport, Twisted loop groups and their affine flag varieties, with an appendix by T. Haines and M. Rapoport, Adv. Math. 219 (2008), 118–198.
  • [19] G. Pappas and M. Rapoport, Local models in the ramified case, III: Unitary groups, J. Inst. Math. Jussieu 8 (2009), 507–564.
  • [20] G. Pappas, M. Rapoport, and B. Smithling, “Local models of Shimura varieties, I: Geometry and combinatorics” in Handbook of Moduli, Vol. III, Int. Press, Somerville, Mass., 2013, 135–217.
  • [21] G. Pappas and X. Zhu, Local models of Shimura varieties and a conjecture of Kottwitz, Invent. Math., published electronically 14 December 2012.
  • [22] M. Rapoport and T. Zink, Period Spaces for p-divisible Groups, Ann. of Math. Stud. 141, Princeton Univ. Press, Princeton, 1996.
  • [23] T. A. Springer, Intersection cohomology of $B\times B$-orbit closures in group compactifications, with an appendix by W. van de Kallen, J. Algebra 258 (2002), 71–111.
  • [24] T. A. Springer, “Some results on compactifications of semisimple groups” in International Congress of Mathematicians, Vol. II, Eur. Math. Soc., Zürich, 2006, 1337–1348.
  • [25] T. A. Springer, “Some subvarieties of a group compactification” in Algebraic Groups and Homogeneous Spaces, Tata Inst. Fund. Res. Stud. Math., Tata Inst. Fund. Res., Mumbai, 2007, 525–543.
  • [26] E. Strickland, A vanishing theorem for group compactifications, Math. Ann. 277 (1987), 165–171.
  • [27] X. Zhu, On the coherence conjecture of Pappas and Rapoport, to appear in Ann. of Math. (2), preprint, arXiv:1012.5979 [math.AG].