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Compactification of the Bruhat-Tits building of PGL by seminorms

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Abstract.

We construct a compactification of the Bruhat-Tits building X associated to the group PGL(V) which can be identified with the space of homothety classes of seminorms on V endowed with the topology of pointwise convergence. Then we define a continuous map from the projective space to which extends the reduction map from Drinfeld’s p-adic symmetric domain to the building X.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Münster, Einsteinstr. 62, 48149, Münster, Germany

    Annette Werner

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  1. Annette Werner
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Correspondence to Annette Werner.

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Mathematics Subject Classification (2000): 20E42, 20G25

in final form: 4 October 2003

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Werner, A. Compactification of the Bruhat-Tits building of PGL by seminorms. Math. Z. 248, 511–526 (2004). https://doi.org/10.1007/s00209-004-0667-7

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  • DOI: https://doi.org/10.1007/s00209-004-0667-7

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