Math @ Duke

Publications [#244105] of Leslie Saper
Papers Published
 Saper, L, Geometric rationality of equalrank Satake compactifications,
Mathematical Research Letters, vol. 11 no. 5
(2004),
pp. 653671, International Press of Boston [MR2106233], [arXiv:math/0211138], [0211138v4], [doi]
(last updated on 2020/04/09)
Abstract: Satake has constructed compactifications of symmetric spaces D=G/K which (under a condition called geometric rationality by Casselman) yield compactifications of the corresponding locally symmetric spaces. The different compactifications depend on the choice of a representation of G. One example is the BailyBorelSatake compactification of a Hermitian locally symmetric space; Baily and Borel proved this is always geometrically rational. Satake compactifications for which all the real boundary components are equalrank symmetric spaces are a natural generalization of the BailyBorelSatake compactification. Recent work (see math.RT/0112250, math.RT/0112251) indicates that this is the natural setting for many results about cohomology of compactifications of locally symmetric spaces. In this paper we prove any Satake compactification for which all the real boundary components are equalrank symmetric spaces is geometrically rational aside from certain rational rank 1 or 2 exceptions; we completely analyze geometric rationality for these exceptional cases. The proof uses Casselman's criterion for geometric rationality. We also prove that a Satake compactification is geometrically rational if the representation is defined over the rational numbers.


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