Slopes of modular forms and the ghost conjecture (unabridged version)

Abstract

We formulate a conjecture on slopes of overconvergent p-adic cuspforms of any p-adic weight in the Gamma_0(N)-regular case. This conjecture unifies a conjecture of Buzzard on classical slopes and more recent conjectures on slopes "at the boundary of weight space".

arXiv comment39 pages, 2 figures, 6 tables. Changes from v1: Removed Section 7 (put on arXiv separately at 1611.01497) and fixed a minor typo in Section 6. We do not plan to publish the paper with this length at this time. This manuscript will be perpetually available, so it is renamed the "unabridged version". A condensed version (absent the combinatorial proofs contained here) will soon be available

References in corpus (7)

• Extended eigenvarieties for overconvergent cohomology
• The eigencurve over the boundary of weight space
• Where the Slopes Are
• Arithmetic properties of Fredholm series for p-adic modular forms
• Spectral expansions of overconvergent modular functions
• Slopes of eigencurves over boundary disks
• A remark on non-integral p-adic slopes for modular forms

Cited by in corpus (4)

• A remark on non-integral p-adic slopes for modular forms
• Generic Newton Slopes for Artin-Schreier-Witt Tower in two variables
• An explicit computation of the Hecke operator and the ghost conjecture
• Class numbers and $p$-ranks in ${\mathbb{Z}}_p^d$-towers