Families of Picard modular forms and an application to the Bloch-Kato conjecture
| Autor: | Hernandez, Valentin |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Compositio Math. 155 (2019) 1327-1401 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/S0010437X1900736X |
| Popis: | In this article we construct a $p$-adic three dimensional Eigenvariety for the group $U(2,1)(E)$, where $E$ is a quadratic imaginary field and $p$ is inert in $E$. The Eigenvariety parametrizes Hecke eigensystems on the space of overconvergent, locally analytic, cuspidal Picard modular forms of finite slope. The method generalized the one developed in Andreatta-Iovita-Pilloni by interpolating the coherent automorphic sheaves when the ordinary locus is empty. As an application of this construction, we reprove a particular case of the Bloch-Kato conjecture for some Galois characters of $E$, extending the result of Bellaiche-Chenevier to the case of a positive sign. Comment: 71 pages |
| Databáze: | arXiv |
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