Lecture----数学院晨兴数学中心

Title:	Boundary of the eigencurve over the weight space(I)
Speaker:	Ruochuan Liu (Peking University)
Time:	2015-4-29, 10:30-11:30
Place:	610
Abstract:	We will explain the proof of 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.
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