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EnglishThe object of this work is to present the status of art of an open problem: to provide an analogue for the cohomology of Shimura curves of the Ihara's lemma which holds for modular curves. We will formulate our conjecture and locate it in the more general setting of the congruence subgroup problem. We will exploit the relationship between cohomology of Shimura curves and certain spaces of modular forms to establish some consequences of the conjecture about congruence modules of modular forms and about the problem of raising the level.
| Titolo: | About an analogue of Ihara's lemma for Shimura curves | |
| Autori Riconosciuti: | ||
| Autori: | Miriam Ciavarella; Lea Terracini | |
| Data di pubblicazione: | 2011 | |
| Abstract: | The object of this work is to present the status of art of an open problem: to provide an analogue for the cohomology of Shimura curves of the Ihara's lemma which holds for modular curves. We will formulate our conjecture and locate it in the more general setting of the congruence subgroup problem. We will exploit the relationship between cohomology of Shimura curves and certain spaces of modular forms to establish some consequences of the conjecture about congruence modules of modular forms and about the problem of raising the level. | |
| Editore: | WYDAWNICTWO NAUKOWE UAM | |
| Titolo del libro: | FUNCTIONES ET APPROXIMATIO: COMMENTARII MATHEMATICI | |
| Collana: | Functiones et Approximatio Commentarii Mathematici | |
| Volume: | 45 | |
| Pagina iniziale: | 23 | |
| Pagina finale: | 41 | |
| ISBN: | 978-83-232-2310-8 | |
| Parole Chiave: | cohomology of Shimura curves, congruence subgroups, Hecke algebras | |
| Appare nelle tipologie: | 02A-Contributo in volume |
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