Theta operators and a generic entailment for $GSp_4$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908770016165888 |
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| author | Ortiz, Martin |
| author_facet | Ortiz, Martin |
| contents | 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 $W(\overlineρ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09602 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theta operators and a generic entailment for $GSp_4$ Ortiz, Martin Number Theory Algebraic Geometry 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 $W(\overlineρ)$. |
| title | Theta operators and a generic entailment for $GSp_4$ |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2410.09602 |