@inbook {MATHEDUC.06089147,
author = {Werner, Annette},
title = {An excursion into the $p$-adic world. (Ein Ausflug in die $p$-adische Welt.)},
year = {2011},
booktitle = {Multifaceted mathematics. Insights into modern mathematical research for all those who want to understand more of mathematics},
isbn = {978-3-8348-1414-2},
pages = {433-451},
publisher = {Wiesbaden: Vieweg+Teubner},
doi = {10.1007/978-3-8348-8173-1_22},
abstract = {This article provides readers with a brief introduction to topics covered in {\it J.-P. Serre}'s book [Trees. Springer Monographs in Mathematics. Berlin: Springer. (2003; Zbl 1013.20001)]. It begins by explaining $p$-adic absolute values, $p$-adic lattices $L$ in the plane, the action of $\mathrm{GL}_2(\Bbb Q)$ on these lattices, and equivalence classes of lattices with respect homothety. By defining when two lattices are ``neighbors'' one is led to the definition of a graph whose vertices are (equivalence classes of) lattices, which are connected by an edge if they are neighbors of each other. The main result is that these graphs $X(p)$ are trees, and that it is possible to study the group $\mathrm{SL}_2(\Bbb Q)$ by investigating its action on this tree.},
reviewer = {Franz Lemmermeyer (Jagstzell)},
msc2010 = {F60xx},
identifier = {2013c.00413},
}