Vol. 289, No. 2, 2017

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Local constancy of dimension of slope subspaces of automorphic forms

Joachim Mahnkopf

Vol. 289 (2017), No. 2, 317–380
DOI: 10.2140/pjm.2017.289.317

We prove an analogue of a Gouvêa–Mazur conjecture on local constancy of dimension of slope subspaces of modular forms on the upper half plane for automorphic forms on reductive algebraic groups G̃ having discrete series. The proof uses a comparison of Bewersdorff’s elementary trace formula for pairs of congruent weights and does not make use of methods from p-adic Banach space theory, overconvergent forms or rigid analytic geometry.

We also compare two Goresky–MacPherson trace formulas computing Lefschetz numbers on weighted cohomology for pairs of congruent weights; this has an application to a more explicit version of the Gouvêa–Mazur conjecture for symplectic groups of rank 2.

Gouvêa–Mazur conjecture, cohomology of arithmetic groups
Mathematical Subject Classification 2010
Primary: 11F75
Received: 27 March 2015
Revised: 20 May 2016
Accepted: 30 May 2016
Published: 19 June 2017
Joachim Mahnkopf
Fakultät für Mathematik
Universität Wien
Oskar-Morgenstern-Platz 1
1190 Wien