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On Ramification of Eigenvarieties

Algebra and Number Theory Seminar

On Ramification of Eigenvarieties
Series: Algebra and Number Theory Seminar
Location: ENR2 S395
Presenter: Chi-Yun Hsu, UCLA

Let D be a totally definite quaternion algebra over a totally real field F. One can consider the eigenvariety attached to D*, which parametrizes p-adic overconvergent Hecke eigenforms of D* of finite slope. In this situation, there is a dual BGG resolution connecting classical forms of dominant weights to overconvergent forms. We explain how to make use of the resolution to relate the ramification behavior of a point of integral weight (not necessarily dominant) and its companion points.