| Título: | the Iwasawa Theory for Unitary groups |
| Autores: | WAN, XIN |
| Fecha: |
2012-08-01 2012-08-01 2012 |
| Publicador: | Princeton, NJ : Princeton University |
| Fuente: |
Ver documento |
| Tipo: | Academic dissertations (Ph.D.) |
| Tema: |
Bloch-Kato conjectures Eisenstein series Iwasawa theory p-adic L-functions Selmer groups Mathematics |
| Descripción: | In this thesis we generalize earlier work of Skinner and Urban to construct ($p$-adic families of) nearly ordinary Klingen Eisensten series for the unitary groups $U(r,s)\hookrightarrow U(r+1,s+1)$ and do some preliminary computations of their Fourier Jacobi coefficients. As an application, using the case of the embedding $U(1,1)\hookrightarrow U(2,2)$ over totally real fields in which the odd prime $p$ splits completely, we prove that for a Hilbert modular form $f$ of parallel weight $2$, trivial character, and good ordinary reduction at all places dividing $p$, if the central critical $L$-value of $f$ is $0$ then the associated Bloch Kato Selmer group has infinite order. We also state a consequence for the Tate module of elliptic curves over totally real fields that are known to be modular. |
| Idioma: | Inglés |
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