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We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group $G$ over a suitable non-Archimedean field $k$ we define a map from the Bruhat-Tits building $ℬ (G, k)$ to the Berkovich analytic space $G^{an}$ associated with $G$ . Composing this map with the projection of $G^{an}$ to its flag varieties, we define a family of compactifications of $ℬ (G, k)$ . This generalizes results by Berkovich in the case of split groups. Moreover,...

Building Buildings.

M.A. Ronan, J. Tits (1987)

Mathematische Annalen

Buildings and non-positively curved polygons of finite groups.

Brown, Paul R. (1998)

The New York Journal of Mathematics [electronic only]

Buildings and shadows.

Betti Salzberg (1982)

Aequationes mathematicae

Calcul du rayon de la sphère inscrite dans le tétraèdre

Georges Dostor (1873)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Caps on Hermitian varieties and maximal curves.

Hirschfeld, J. W. P., Korchmáros, G. (2003)

Advances in Geometry

Chamber systems, geometries and parabolic systems whose diagram contains only bonds of strength 1 and 2.

G. Stroth (1990)

Inventiones mathematicae

Charakterisierung der kompakten, zusammenhängenden Moufang-Hughes-Ebenen anhand ihrer Kollineationen.

Hermann Hähl (1986)

Mathematische Zeitschrift

Classification of flocks of the quadratic cone over fields of order at most 29.

Law, M., Penttila, T. (2003)

Advances in Geometry

Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Baicheva, Tsonka, Topalova, Svetlana (2015)

Serdica Journal of Computing

Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant...

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Baer-Elation planes

Blocking set nei piani proiettivi

Blocking sets in $P G (2, q)$ for small $p$ , and partial spreads in $P G (3, 7)$ .

Blocking sets of 16 points in projective planes of order 10 - III

Blocking sets of maximal type in finite projective planes

Blocking sets which are preserved by transitive collineation groups.

Bruhat-Tits theory from Berkovich’s point of view. I. Realizations and compactifications of buildings