2024/10/12 by Ortiz, Martin · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2410.09602
openalex publication_date 2024/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a new family of mod p weight shifting differential operators on the Siegel threefold. In particular, we construct one operator which generalizes the classical theta cycle, whose weight shift allows for maps between p-restricted weights, and which is generically injective on global sections. As an application we produce a generic entailment of Serre weights, i.e. any Hecke eigenform which is modular for a generic Serre weight in the lowest alcove is also modular for a Serre weight in one of the upper alcoves. The entailed Serre weight corresponds to a shadow weight of the lowest alcove Serre weight, in Herzig's conjectural description of W(ρ).