Lifting non-ordinary cohomology classes for \(\mathrm{SL}_3\). (English) Zbl 1440.11089

Summary: In this paper, we present a generalisation of a theorem of D. Pollack and R. Pollack. In [Can. J. Math. 61, No. 3, 674–690 (2009; Zbl 1228.11074)], they give a very general argument for lifting ordinary eigenclasses (with respect to a suitable operator) in the group cohomology of certain arithmetic groups. With slightly tighter conditions, we prove the same result for non-ordinary classes. Pollack and Pollack apply their results to the case of \(p\)-ordinary classes in the group cohomology of congruence subgroups for \(\mathrm{SL}_3\), constructing explicit overconvergent classes in this setting. As an application of our results, we give an extension of their results to the case of non-critical slope classes in the same setting.


11F75 Cohomology of arithmetic groups
11F85 \(p\)-adic theory, local fields


Zbl 1228.11074
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