Profinite invariants of arithmetic groups. (13th November 2020)

• Record Type: Journal Article
• Authors: Kammeyer, Holger; Kionke, Steffen; Raimbault, Jean; Sauer, Roman
• Is Part Of: Forum of mathematics. Volume 8(2020)
• Publication Date: 2020-11-13
• Subjects: profinite rigidity, -- arithmetic groups, -- l2-invariants; 20E18, -- 11F75; Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2020.43
• Languages: English
• ISSNs: 2050-5094

Abstract

Abstract: We prove that the sign of the Euler characteristic of arithmetic groups with the congruence subgroup property is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself and that the sign of the Euler characteristic is not profinite among general residually finite groups of type F . Our methods imply similar results for $\ell^2$ -torsion as well as a strong profiniteness statement for Novikov–Shubin invariants.