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arXiv · 2006.15106

Congruences of Eisenstein series of level $Γ_1(N)$ via Dieudonné theory of formal groups

Ningchuan Zhang
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Abstract

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 $1$.

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Ningchuan Zhang. 2024-11-30. Congruences of Eisenstein series of level $Γ_1(N)$ via Dieudonné theory of formal groups. https://doi.org/10.5802/jtnb.1277

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