Open Access
2018 Lifting non-ordinary cohomology classes for $\mathrm{SL}_3$
Chris Williams
Publ. Mat. 62(2): 651-675 (2018). DOI: 10.5565/PUBLMAT6221810


In this paper, we present a generalisation of a theorem of David and Rob Pollack. In [PP], 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.


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Chris Williams. "Lifting non-ordinary cohomology classes for $\mathrm{SL}_3$." Publ. Mat. 62 (2) 651 - 675, 2018.


Received: 23 February 2017; Revised: 13 July 2017; Published: 2018
First available in Project Euclid: 16 June 2018

zbMATH: 06918959
MathSciNet: MR3815291
Digital Object Identifier: 10.5565/PUBLMAT6221810

Primary: 11F75
Secondary: 11F85

Keywords: $\mathrm{SL}_3$ , control theorem , modular symbols , overconvergent

Rights: Copyright © 2018 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.62 • No. 2 • 2018
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