Equivariant Torsion and Base Change

2013/12/09 by Michael Lipnowski, Lipnowski, Michael
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1312.2540

Abstract

What is the true order of growth of torsion in the cohomology of an arithmetic group? Let D be a quaternion over an imaginary quadratic field F. Let E/F be a cyclic Galois extension with Gal(E/F) = ⟨ σ⟩. We prove lower bounds for "the Lefschetz number of σ acting on torsion cohomology" of certain Galois-stable arithmetic subgroups of D_E^×. For these same subgroups, we unconditionally prove a would-be-numerical consequence of the existence of a hypothetical base change map for torsion cohomology.

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