dc.contributor.advisor Kisin, Mark dc.contributor.author Ye, Lynnelle Lin dc.date.accessioned 2019-12-12T08:59:04Z dc.date.created 2019-05 dc.date.issued 2019-05-03 dc.date.submitted 2019 dc.identifier.citation Ye, Lynnelle Lin. 2019. Slopes in eigenvarieties for definite unitary groups. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences. dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029693 * dc.description.abstract We 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.sponsorship Mathematics dc.format.mimetype application/pdf dc.language.iso en dash.license LAA dc.subject p-adic automorphic forms dc.subject eigenvarieties dc.subject eigencurve dc.title Slopes in eigenvarieties for definite unitary groups dc.type Thesis or Dissertation dash.depositing.author Ye, Lynnelle Lin dc.date.available 2019-12-12T08:59:04Z thesis.degree.date 2019 thesis.degree.grantor Graduate School of Arts & Sciences thesis.degree.grantor Graduate School of Arts & Sciences thesis.degree.level Doctoral thesis.degree.level Doctoral thesis.degree.name Doctor of Philosophy thesis.degree.name Doctor of Philosophy dc.contributor.committeeMember Mazur, Barry dc.contributor.committeeMember Miller, Alison dc.type.material text thesis.degree.department Mathematics thesis.degree.department Mathematics dash.identifier.vireo dash.author.email lynnelle.lin.ye@gmail.com
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