Vol. 9, No. 10, 2015

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Equivariant torsion and base change

Michael Lipnowski

Vol. 9 (2015), No. 10, 2197–2240
Abstract

What is the true order of growth of torsion in the cohomology of an arithmetic group? Let D be a quaternion algebra over an imaginary quadratic field F. Let EF be a cyclic Galois extension with ΓEF = σ. We prove lower bounds for “the Lefschetz number of σ acting on torsion cohomology” of certain Galois-stable arithmetic subgroups of DE×. For these same subgroups, we unconditionally prove a would-be-numerical consequence of the existence of a hypothetical base change map for torsion cohomology.

Keywords
torsion, cohomology, Reidemeister torsion, analytic torsion, Ray–Singer torsion, locally symmetric space, trace formula, base change, equivariant, twisted
Mathematical Subject Classification 2010
Primary: 11F75
Secondary: 11F72, 11F70
Milestones
Received: 13 May 2014
Revised: 21 July 2015
Accepted: 6 October 2015
Published: 16 December 2015
Authors
Michael Lipnowski
Mathematics Department
Duke University
Duke University, Box 90320
Durham, NC 27708-0320
United States