CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 11F75 ( Cohomology of arithmetic groups )

  Expand all        Collapse all Results 1 - 1 of 1

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

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/