TY - BOOK AU - Witzel,Stefan TI - Finiteness properties of arithmetic groups acting on twin buildings T2 - Lecture notes in mathematics SN - 9783319064765 U1 - 512.2 23 PY - 2014/// CY - New York PB - Springer KW - Buildings (Group theory) KW - Finite geometries. N1 - Includes bibliographical references and index; 1. Basic Definitions and Properties -- 2. Finiteness Properties of G(Fq[t]) -- 3. Finiteness Properties of G(Fq[t; t-1]) -- A Adding places-- References-- Index of symbols-- Index N2 - Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings ER -