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Compactification of the Bruhat-Tits building of PGL by seminorms. (English) Zbl 1121.20024
Summary: We construct a compactification $$\overline X$$ of the Bruhat-Tits building $$X$$ associated to the group $$\text{PGL}(V)$$ 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 $$\overline X$$ which extends the reduction map from Drinfeld’s $$p$$-adic symmetric domain to the building $$X$$.

##### MSC:
 20E42 Groups with a $$BN$$-pair; buildings 20G25 Linear algebraic groups over local fields and their integers
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##### References:
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