Mixed modular symbols and the generalized cuspidal $1$-motive
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- by Emmanuel Lecouturier PDF
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Abstract:
We define and study the space of mixed modular symbols for a given finite index subgroup $\Gamma$ of $\operatorname {SL}_2(\mathbf {Z})$. This is an extension of the usual space of modular symbols that, in some cases, carries more information about Eisenstein series. We make use of mixed modular symbols to construct some $1$-motives related to the generalized Jacobian of modular curves. In the case $\Gamma = \Gamma _0(p)$ for some prime $p$, we relate our construction to the work of Ehud de Shalit on $p$-adic periods of $X_0(p)$.References
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Additional Information
- Emmanuel Lecouturier
- Affiliation: Yau Mathematical Sciences Center and Department of mathematics, Tsinghua University, Beijing, People’s Republic of China
- MR Author ID: 969451
- Received by editor(s): July 20, 2019
- Received by editor(s) in revised form: July 6, 2020, July 28, 2020, and August 11, 2020
- Published electronically: February 8, 2021
- Additional Notes: This research was funded by Tsinghua University and the Yau Mathematical Sciences Center
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 374 (2021), 2823-2872
- MSC (2020): Primary 11Fxx
- DOI: https://doi.org/10.1090/tran/8310
- MathSciNet review: 4223035