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dc.contributor.advisorKisin, Mark
dc.contributor.authorYe, Lynnelle Lin
dc.date.accessioned2019-12-12T08:59:04Z
dc.date.created2019-05
dc.date.issued2019-05-03
dc.date.submitted2019
dc.identifier.citationYe, Lynnelle Lin. 2019. Slopes in eigenvarieties for definite unitary groups. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:42029693*
dc.description.abstractWe generalize bounds of Liu-Wan-Xiao for slopes in eigencurves for definite unitary groups of rank $2$, which formed the core of their proof of the Coleman-Mazur-Buzzard-Kilford conjecture about the decomposition of the eigencurve over the boundary of weight space, to eigenvarieties for definite unitary groups of any rank. We show that for a definite unitary group of rank $n$, the Newton polygon of the characteristic power series of the $U_p$ Hecke operator has exact polynomial growth rate $x^{1+\frac2{n(n-1)}}$, with constant proportional to the distance of the weight from the boundary of weight space. This improves a previous lower bound of $x^{1+\frac1{2^n-n-1}}$ of Chenevier (which applied only to the center of weight space). The proof goes through the classification of forms associated to principal series representations. We also give a consequence for the geometry of these eigenvarieties over the boundary of weight space.
dc.description.sponsorshipMathematics
dc.format.mimetypeapplication/pdf
dc.language.isoen
dash.licenseLAA
dc.subjectp-adic automorphic forms
dc.subjecteigenvarieties
dc.subjecteigencurve
dc.titleSlopes in eigenvarieties for definite unitary groups
dc.typeThesis or Dissertation
dash.depositing.authorYe, Lynnelle Lin
dc.date.available2019-12-12T08:59:04Z
thesis.degree.date2019
thesis.degree.grantorGraduate School of Arts & Sciences
thesis.degree.grantorGraduate School of Arts & Sciences
thesis.degree.levelDoctoral
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
thesis.degree.nameDoctor of Philosophy
dc.contributor.committeeMemberMazur, Barry
dc.contributor.committeeMemberMiller, Alison
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.departmentMathematics
dash.identifier.vireo
dash.author.emaillynnelle.lin.ye@gmail.com


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