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Title: the Iwasawa Theory for Unitary groups
Authors: WAN, XIN
Advisors: Skinner, Christopher
Contributors: Mathematics Department
Keywords: Bloch-Kato conjectures
Eisenstein series
Iwasawa theory
p-adic L-functions
Selmer 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.
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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