Prasad, Gopal ; Yeung, Sai-Kee (2009) Arithmetic fake projective spaces and arithmetic fake Grassmannians American Journal of Mathematics, 131 (2). pp. 379-407. ISSN 0002-9327
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Official URL: http://www.jstor.org/stable/40263772
Related URL: http://dx.doi.org/10.1353/ajm.0.0043
Abstract
In a recent paper we have classified fake projective planes. Natural higher dimensional generalization of these surfaces are arithmetic fake $P_c^{n - 1} $ , and arithmetic fake $Gr_{m,n.} $ In this paper we show that arithmetic fake $P_c^{n - 1} $ can exist only if n = 3, 5, and an arithmetic fake $Gr_{m,n.} $ can exist, with n > 3 odd, only if n = 5. Here we construct four distinct arithmetic fake $P_c^4 ,$ , and four distinct fake arithmetic $Gr_{2,5\,\cdot} $ Furthermore, we use certain results and computations of [PY] to exhibit five irreducible arithmetic fake $P_c^2 \times P_{c\cdot}^2 $ All these are connected smooth (complex projective) Shimura varieties.
Item Type: | Article |
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Source: | Copyright of this article belongs to Johns Hopkins University Press. |
ID Code: | 36775 |
Deposited On: | 04 Jul 2012 13:30 |
Last Modified: | 17 May 2016 19:42 |
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