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arXiv 2204.13086math.KT
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关于正特征格的有理同调维数的注记

A note on the rational homological dimension of lattices in positive characteristic

Sam Hughes

摘要:

通过$\ell^2$ -同调证明了在全局函数域上的单连通Chevalley群的乘积格的有理同调维数等于有理上同调维数和相应的Bruhat-Tits建筑的维数.

英文摘要:

We show via $\ell^2$-homology that the rational homological dimension of a lattice in a product of simple simply connected Chevalley groups over global function fields is equal to the rational cohomological dimension and to the dimension of the associated Bruhat--Tits building.

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