Kisin, MarkDiao, Hansheng2014-06-062014-06-062014Diao, Hansheng. 2014. The Eigencurve is Proper. Doctoral dissertation, Harvard University.http://dissertations.umi.com/gsas.harvard:11592http://nrs.harvard.edu/urn-3:HUL.InstRepos:12271809Coleman and Mazur constructed a rigid analytic curve Cp,N, called the eigencurve, whose points correspond to all finite slope overconvergent p-adic eigenforms. We prove the conjecture that the eigencurve Cp,N is proper over the weight space for any prime p and tame level N.en-USMathematicsThesis or Dissertation2014-06-06