A Construction of Rigid Analytic Cohomology Classes for Congruence Subgroups of SL3(Z)

Pollack, David ; Pollack, Robert

Canadian journal of mathematics, Tome 61 (2009) no. 3, pp. 674-690

Résumé

We give a constructive proof, in the special case of $\text{G}{{\text{L}}_{3}}$ , 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.

Détail

DOI : 10.4153/CJM-2009-036-0

Mots-clés : 11F75, 11F85

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