Slopes in eigenvarieties for definite unitary groups

2020/04/26 by Ye, Lynnelle
#11F55 (Secondary) #11F85 (Primary) 11F70 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.12490

Abstract

We generalize bounds of Liu-Wan-Xiao for slopes in eigencurves for definite unitary groups of rank 2 to slopes in 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 growth rate x^1+\frac2n(n-1), times a constant proportional to the distance of the weight from the boundary 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.

Related

• Slopes of eigencurves over boundary disks
• Endoscopic transfer between eigenvarieties for definite unitary groups
• Where the Slopes Are
• Spectral gaps, critical exponents and representations of negatively curved groups
• Companion points on the eigenvariety with non-regular weights