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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01c534fn974
 Title: the Iwasawa Theory for Unitary groups Authors: WAN, XIN Advisors: Skinner, Christopher Contributors: Mathematics Department Keywords: Bloch-Kato conjecturesEisenstein seriesIwasawa theoryp-adic L-functionsSelmer groups Subjects: Mathematics Issue Date: 2012 Publisher: Princeton, NJ : Princeton University Abstract: 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. URI: http://arks.princeton.edu/ark:/88435/dsp01c534fn974 Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics

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