Eichler–Shimura isomorphism and group cohomology on arithmetic groups
| Autor: | Santiago Molina |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| Rok vydání: | 2017 |
| Předmět: |
Automorphic forms
Discrete mathematics Group isomorphism Algebra and Number Theory Quaternion algebra Eichler–Shimura isomorphism Multiplicative group Mathematics::Number Theory Group cohomology 010102 general mathematics Automorphic form Nombres Teoria dels 01 natural sciences 11 Number theory::11U Connections with logic [Classificació AMS] Combinatorics Morphism Number theory 0103 physical sciences Eichler-Shimura Homomorphism 010307 mathematical physics Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC] 0101 mathematics Mathematics |
| Zdroj: | RECERCAT (Dipòsit de la Recerca de Catalunya) Recercat. Dipósit de la Recerca de Catalunya instname Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2017.04.007 |
| Popis: | In this article, we give a group cohomological interpretation to the Eichler–Shimura isomorphism. For any quaternion algebra A over a totally real field with multiplicative group G , we interpret a weight ( k 1 , k 2 , ⋯ , k d ) -automorphic form of G as a G ( F ) -invariant homomorphism of ( G ∞ , K ∞ ) -modules. Then the Eichler–Shimura isomorphism is given by the connection morphism provided by the natural exact sequences defining the ( G ∞ , K ∞ ) -module of discrete series of weight ( k 1 , k 2 , ⋯ , k d ) . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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