Equivariant Torsion and Base Change

Michael Lipnowski

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arXiv · 1312.2540

Equivariant Torsion and Base Change

Michael Lipnowski

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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 $\mathrm{Gal}(E/F) = \langle \sigma \rangle.$ 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.

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Michael Lipnowski. 2013-12-09. Equivariant Torsion and Base Change. https://arxiv.org/abs/1312.2540

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