Descent of affine buildings - I. Large minimal angles

Mühlherr, Bernhard; Struyve, Koen; Maldeghem, Hendrik Van

doi:10.1090/s0002-9947-2014-05985-0

Cited by 3 publications

(2 citation statements)

References 31 publications

(37 reference statements)

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“…Let us recapitulate what we already had obtained in Section 5.2 of Part I ( [8]). We there constructed a subset Λ ′ of the completion of Λ, together with a set of injections from an Euclidean space (which is in the present case the real line) to this set.…”

Section: Additional Definitions and Notationsmentioning

confidence: 74%

“…Applying the methods from Section 5.2 of [8] to I E,ω (G) and the Galois involution acting on it, one obtains a subset Λ ′ of the points of I E,ω (G). We make the special choice of fixed point as outlined in Remark 5.5 of [8]. This has as advantage that isometries of I E,ω (G) centralizing the Galois involution stabilize Λ ′ .…”

Section: An Algebraic Proofmentioning

confidence: 99%

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Descent of affine buildings - II. Minimal angle $\pi /3$ and exceptional quadrangles

Struyve

2014

Trans. Amer. Math. Soc.

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In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture concerning the existence of affine buildings arising from such groups defined over a (skew) field with a complete valuation, as proposed by Jacques Tits.This second part builds upon the results of the first part and deals with the remaining cases.

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Section: Additional Definitions and Notationsmentioning

confidence: 74%

Section: An Algebraic Proofmentioning

confidence: 99%

Descent of affine buildings - II. Minimal angle $\pi /3$ and exceptional quadrangles

Struyve

2014

Trans. Amer. Math. Soc.

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Ramified automorphic induction and zero-dimensional affine Deligne–Lusztig varieties

Ivanov

2017

Math. Z.

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To any connected reductive group G over a non-archimedean local field F (of characteristic p ą 0) and to any maximal torus T of G, we attach a family of extended affine Deligne-Lusztig varieties (and families of torsors over them) over the residue field of F . This construction generalizes affine Deligne-Lusztig varieties of Rapoport, which are attached only to unramified tori of G. Via this construction, we can attach to any maximal torus T of G and any character of T a representation of G. This procedure should conjecturally realize the automorphic induction from T to G.For G " GL2, we prove that our construction indeed realizes the automorphic induction from at most tamely ramified tori. Moreover, if the torus is purely tamely ramified, then the varieties realizing this correspondence are zero-dimensional and reduced, i.e., just disjoint unions of points. T of GpF q over Q . Moreover, R χ T is supercuspidal, whenever T is anisotropic modulo the center of G. Such a correspondence is a special case of the more general principle of automorphic induction for G, which is closely related to the local Langlands correspondence.Let G again be arbitrary. Roughly, one can divide all geometrical objects attached to G, in the cohomology of which one has tried to realize the automorphic induction, into two types: (i) Varieties (or rigid or adic spaces) over Spec F equipped with integral models over Spec O F and special fibers over F q . (ii) Reduced varieties over F q .Constructions of type (ii) are purely in characteristic p, i.e., over F q , and only the reduced structure is relevant. Up to now, constructions of type (ii) only existed for unramified tori of

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On triples of ideal chambers in A2-buildings

Parreau

2019

Innov. Incidence Geom.

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We investigate the geometry in a real Euclidean building X of type A2 of some simple configurations in the associated projective plane at infinity P, seen as ideal configurations in X, and relate it with the projective invariants (from the cross ratio on P). In particular we establish a geometric classification of generic triples of ideal chambers of X and relate it with the triple ratio of triples of flags. arXiv:1504.00285v1 [math.MG] 1 Apr 2015

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Descent of affine buildings - I. Large minimal angles

Cited by 3 publications

References 31 publications

Descent of affine buildings - II. Minimal angle $\pi /3$ and exceptional quadrangles

Descent of affine buildings - II. Minimal angle $\pi /3$ and exceptional quadrangles

Ramified automorphic induction and zero-dimensional affine Deligne–Lusztig varieties

On triples of ideal chambers in A2-buildings

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