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math.NT2022
The slope-invariant of local ghost series under direct sum
Rufei Ren
The ghost conjecture is first provided by Bergdall and Pollack in [BP-1,BP-2] to study the Up-slopes of spaces of modular forms, which, so far, has already brought plenty of import…
math.NT2022
Localized Gouvêa-Mazur conjecture
Rufei Ren
Gouvêa-Mazur [GM] made a conjecture on the local constancy of slopes of modular forms when the weight varies -adically. Since one may decompose the space of modular forms accord…