SL_n Z的余维1上同调
The codimension-one cohomology of SL_n Z
摘要：
证明了H^{d-1}（SL_n Z; Q）= 0，其中d = n-choose-2是SL_n Z的上同调维数，GL_n Z也是如此.我们还证明了系数在代数群GL_n的有理表示中的上同调的类似消灭定理。这些定理是由SL_n Z的Steinberg模的一个表示导出的，它的生成元是整公寓类，推广了Manin关于SL_2 Z的Steinberg模的一个表示.这个演示文稿最初由Bykovskii构建。我们给出了一个新的拓扑证明。
英文摘要：
We prove that H^{d-1}(SL_n Z; Q) = 0, where d = n-choose-2 is the cohomological dimension of SL_n Z, and similarly for GL_n Z. We also prove analogous vanishing theorems for cohomology with coefficients in a rational representation of the algebraic group GL_n. These theorems are derived from a presentation of the Steinberg module for SL_n Z whose generators are integral apartment classes, generalizing Manin's presentation for the Steinberg module of SL_2 Z. This presentation was originally constructed by Bykovskii. We give a new topological proof of it.
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