Eigencurve over the boundary of the weight space
主 题: Eigencurve over the boundary of the weight space
报告人: 刘若川 (北京国际数学研究中心研究员)
时 间: 2015-04-26 14:00 - 14:45
地 点: 澳门皇冠金沙网站十大镜春园82号甲乙丙楼二层报告厅
We will prove a folklore conjecture concerning the geometry of the boundary of eigencurves in the case of definite quaternion algebras over Q. Precisely, we prove that: (a) over the boundary annuli of the weight space, the eigencurve is a disjoint union of (countably) infinitely many connected components each finite and flat over the weight annuli, (b) the Up-slopes of points on each fixed connected component are proportional to the p-adic valuations of the parameter on the weight space, and (c) the sequence of the slope ratios form a union of finitely many arithmetic progressions with the same common difference. Joint work with Daqing Wan and Liang Xiao.