Congruences of Eisenstein series of level $Γ_1(N)$ via Dieudonné theory of formal groups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866912138108338176 |
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| author | Zhang, Ningchuan |
| author_facet | Zhang, Ningchuan |
| contents | In this paper, we give a new explanation of congruences of Eisenstein series of level $Γ_1(N)$ and character $χ$. Our approach is based on Katz's algebro-geometric explanation of $p$-adic congruences of normalized Eisenstein series $E_{2k}$ of level $1$. One crucial step in our argument is to reformulate a Riemann-Hilbert correspondence in Katz's explanation in terms of Dieudonné theory of height $1$ formal $A$-modules and their finite subgroup schemes. We give a generalization of this Riemann-Hilbert correspondence in terms of formal groups of height greater than $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_15106 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Congruences of Eisenstein series of level $Γ_1(N)$ via Dieudonné theory of formal groups Zhang, Ningchuan Number Theory Algebraic Geometry Algebraic Topology 11F33, 14L05 In this paper, we give a new explanation of congruences of Eisenstein series of level $Γ_1(N)$ and character $χ$. Our approach is based on Katz's algebro-geometric explanation of $p$-adic congruences of normalized Eisenstein series $E_{2k}$ of level $1$. One crucial step in our argument is to reformulate a Riemann-Hilbert correspondence in Katz's explanation in terms of Dieudonné theory of height $1$ formal $A$-modules and their finite subgroup schemes. We give a generalization of this Riemann-Hilbert correspondence in terms of formal groups of height greater than $1$. |
| title | Congruences of Eisenstein series of level $Γ_1(N)$ via Dieudonné theory of formal groups |
| topic | Number Theory Algebraic Geometry Algebraic Topology 11F33, 14L05 |
| url | https://arxiv.org/abs/2006.15106 |