Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01g158bk68k
 Title: On local-global compatibility for cuspidal regular algebraic automorphic representations of GLn Authors: Varma, Ila Advisors: Taylor, RichardBhargava, Manjul Contributors: Mathematics Department Keywords: Galois representationsLanglands programp-adic automorphic forms Subjects: Mathematics Issue Date: 2015 Publisher: Princeton, NJ : Princeton University Abstract: We prove the compatibility of local and global Langlands correspondences for $\GL_n$ up to semisimplification for the Galois representations constructed by Harris-Lan-Taylor-Thorne and Scholze. More precisely, let $r_p(\pi)$ denote an $n$-dimensional $p$-adic representation of the Galois group of a CM field $F$ attached to a regular algebraic cuspidal automorphic representation $\pi$ of $\GL_n(\bA_F)$. We show that the restriction of $r_p(\pi)$ to the decomposition group of a place $v\nmid p$ of $F$ corresponds up to semisimplification to $\rec(\pi_v)$, the image of $\pi_v$ under the local Langlands correspondence. Furthermore, we can show that the monodromy of the associated Weil-Deligne representation of $\left.r_p(\pi)\right|_{\Gal_{F_v}}$ is `more nilpotent' than the monodromy of $\rec(\pi_v)$. URI: http://arks.princeton.edu/ark:/88435/dsp01g158bk68k Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: http://catalog.princeton.edu/ Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics

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