Abstract
We consider modifications of Manin symbols in first homology groups of modular curves with Zp-coefficients for an odd prime p. We show that these symbols generate homology in primitive eigenspaces for the action of diamond operators, with a certain condition on the eigenspace that can be removed on Eisenstein parts. We apply this to prove the integrality of maps taking compatible systems of Manin symbols to compatible systems of zeta elements. In the work of the first two authors on an Iwasawa-theoretic conjecture of the third author, these maps are constructed with certain bounded denominators. As a consequence, their main result on the conjecture was proven after inverting p, and the results of this paper allow one to remove this condition.
Original language | English (US) |
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Pages (from-to) | 377-395 |
Number of pages | 19 |
Journal | Annales Mathematiques du Quebec |
Volume | 40 |
Issue number | 2 |
DOIs | |
State | Published - Aug 1 2016 |
Keywords
- Eisenstein ideals
- Hecke algebras
- Iwasawa theory
- Modular symbols
ASJC Scopus subject areas
- General Mathematics