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arXiv · 1905.05260

Torsions in Cohomology of $\text{SL}_2(\mathbb{Z})$ and Congruence of Modular Forms

Taiwang Deng
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Abstract

We describe torsion classes in the first cohomology group of $\text{SL}_2(\mathbb{Z})$. In particular, we obtain generalized Dickson's invariants for p-power polynomial rings. Secondly, we describe torsion classes in the zero-th homology group of $\text{SL}_2(\mathbb{Z})$ as a module over the torsion invariants. As application, we obtain various congruences between cuspidal forms of level one and Eisenstein series.

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Taiwang Deng. 2019-05-13. Torsions in Cohomology of $\text{SL}_2(\mathbb{Z})$ and Congruence of Modular Forms. https://arxiv.org/abs/1905.05260

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