Rational discrete cohomology for totally disconnected locally compact groups

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• 作者：I. Castellano^a ; ^{ilaria.castellano@uniba.it" class="auth_mail" title="E-mail the corresponding author} ; Th. Weigel^b ; ^{thomas.weigel@unimib.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20J06 ; 22D05 ; 57T99 ; 22E20 ; 51E42 ; 17B67
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：453
• 期：Complete
• 页码：101-159
• 全文大小：907 K

文摘

Rational discrete cohomology and homology for a totally disconnected locally compact group G   are introduced and studied. The Hom-⊗ identity associated to the rational discrete bimodule Bi(G)$\mathrm{Bi}(G)$ allows to introduce the notion of rational duality group in analogy to the discrete case. It is shown that a semi-simple algebraic group G(K)$G(K)$ defined over a non-discrete, non-archimedean local field K   is a rational t.d.l.c. duality group, and the same is true for certain topological Kac–Moody groups. Indeed, for these groups the Tits (or Davis) realization of the associated building is a finite-dimensional model of the classifying space 20dd7e33">${\underset{\_}{E}}_{\mathfrak{C}}(G(K))$ one may define for any t.d.l.c. group. In contrast, Y. Neretin's group of spheromorphisms of a locally finite regular tree is not even of finite rational discrete cohomological dimension.