Document Type
Article
Version
Author's Final Manuscript
Publication Title
International Mathematics Research Notices
Volume
rnx141
Publication Date
2017
Abstract
We formulate a conjecture on slopes of overconvergent p" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline-table; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">p-adic cusp forms of any p" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline-table; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">p-adic weight in the Γ0(N)" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline-table; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">Γ0(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.”
Citation
Berdall, John and Robert Pollack. 2017. "Slopes of modular forms and the ghost conjecture." International Mathematics Research Notices, rnx141.
DOI
https://doi.org/10.1093/imrn/rnx141