Motivic congruences and Sharifi's conjecture
Let f be a cuspidal eigenform of weight two and level N , let p N be a prime at which f is congruent to an Eisenstein series and let V(f )denote the p-adic Tate module off. Beilinson constructed a class kappa f is an element of H-1(Q,Vf(1)) arising from the cup product of two Siegel units and proved...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/482419 |
| Acceso en línea: | http://hdl.handle.net/2072/482419 |
| Access Level: | acceso abierto |
| Palabra clave: | Motivic Congruences 51 |
| Sumario: | Let f be a cuspidal eigenform of weight two and level N , let p N be a prime at which f is congruent to an Eisenstein series and let V(f )denote the p-adic Tate module off. Beilinson constructed a class kappa f is an element of H-1(Q,Vf(1)) arising from the cup product of two Siegel units and proved a striking relationship with the first derivative L '(f, 0) at the near central point s = 0 of the L-series of f , which led him to formulate his celebrated conjecture. In this note we prove two congruence formulae relating the motivic part of L '(f, 0) ( mod p) and L ''(f, 0) ( mod p) with circular units. The proofs make use of delicate Galois properties satisfied by various integral lattices within V(f )and exploits Perrin-Riou's, Coleman's and Kato's work on the Euler systems of circular units and Beilinson-Kato elements and, most crucially, the work of Sharifi, Fukaya-Kato, and Ohta. |
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