Editing Building (mathematics) (section)

===Bruhat–Tits trees with complex multiplication===

When {{mvar|L}} is an archimedean local field then on the building for the group {{math|SL<sub>2</sub>(''L'')}} an additional structure can be imposed of a building with complex multiplication. These were first introduced by [[Martin L. Brown]]  ({{harvnb|Brown|2004}}). These buildings arise when a quadratic extension of {{mvar|L}} acts on the vector space {{math|''L''<sup>2</sup>}}. These building with complex multiplication can be extended to any global field. They  describe  the action of the Hecke operators on  Heegner points on the classical modular curve {{math|''X''<sub>0</sub>(''N'')}} as well as on the Drinfeld modular curve {{math|''X''{{su|b=0|p=Drin}}(''I'')}}. These buildings with complex multiplication are completely classified for the case of {{math|SL<sub>2</sub>(''L'')}} in {{harvnb|Brown|2004}}