Kisin, MarkKnight, Erick Phillip2019-08-092017-052017-05-162017Knight, Erick Phillip. 2017. A p-adic Jacquet-Langlands Correspondence. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.http://nrs.harvard.edu/urn-3:HUL.InstRepos:41141525In this paper, we construct a candidate p-adic Jacquet-Langlands correspondence. This is a correspondence between unitary continuous admissible representations of GL2(Qp) valued in p-adic Banach spaces, and unitary continuous representations of D× valued in p-adic Banach spaces. Here, D is the quaternion algebra over Qp. The characterizing properties that are shown are a local-global compatibility and a calculation of the locally algebraic vectors.application/pdfenNumber TheoryThesis or Dissertation2019-08-09