Equivariant Torsion and Base Change

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 $\mathrm{Gal}(E/F)=⟨\sigma ⟩.$ We prove lower bounds for "the Lefschetz number of $\sigma$ acting on torsion cohomology" of certain Galois-stable arithmetic subgroups of $D_E^{\times }.$ For these same subgroups, we unconditionally prove a would-be-numerical consequence of the existence of a hypothetical base change map for torsion cohomology.

47 pages

References in corpus (1)

• A torsion Jacquet--Langlands correspondence