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Preprints, Working Papers, ... Year : 2024

$\Lambda$-buildings associated to quasi-split groups over $\Lambda$-valued fields

Abstract

Let $\mathbf{G}$ be a quasi-split reductive group and $\mathbb{K}$ be a Henselian field equipped with a valuation $\omega:\mathbb{K}^{\times}\rightarrow \Lambda$, where $\Lambda$ is a totally ordered abelian group. In 1972, Bruhat and Tits constructed a building on which the group $\mathbf{G}(\mathbb{K})$ acts provided that $\Lambda$ is a subgroup of $\mathbb{R}$. In this paper, we deal with the general case where there are no assumptions on $\Lambda$ and we construct a set on which $\mathbf{G}(\mathbb{K})$ acts. We then prove that it is a $\Lambda$-building, in the sense of Bennett.
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Dates and versions

hal-02430546 , version 1 (07-01-2020)
hal-02430546 , version 2 (16-06-2020)
hal-02430546 , version 3 (01-02-2024)

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Cite

Auguste Hébert, Diego Izquierdo, Benoît Loisel. $\Lambda$-buildings associated to quasi-split groups over $\Lambda$-valued fields. 2024. ⟨hal-02430546v3⟩
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