TL;DR
This paper surveys recent progress and challenges in understanding the p-adic slopes of modular forms, discussing strategies for future research and related open questions.
Contribution
It provides a comprehensive overview of the current state of research on p-adic slopes of modular forms and explores potential directions for advancing the field.
Findings
Summarizes recent progress in p-adic slope research
Identifies key challenges and open questions
Proposes strategies for future investigations
Abstract
We survey the progress (or lack thereof!) that has been made on some questions about the p-adic slopes of modular forms that were raised by the first author in [Buz05], discuss strategies for making further progress, and examine other related questions.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Advanced Mathematical Identities