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1. CJM 2009 (vol 61 pp. 674)

Pollack, David; Pollack, Robert
A Construction of Rigid Analytic Cohomology Classes for Congruence Subgroups of $\SL_3(\mathbb Z)$
We give a constructive proof, in the special case of ${\rm GL}_3$, of a theorem of Ash and Stevens which compares overconvergent cohomology to classical cohomology. Namely, we show that every ordinary classical Hecke-eigenclass can be lifted uniquely to a rigid analytic eigenclass. Our basic method builds on the ideas of M. Greenberg; we first form an arbitrary lift of the classical eigenclass to a distribution-valued cochain. Then, by appropriately iterating the $U_p$-operator, we produce a cocycle whose image in cohomology is the desired eigenclass. The constructive nature of this proof makes it possible to perform computer computations to approximate these interesting overconvergent eigenclasses.

Categories:11F75, 11F85

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