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Wednesday 12/4/02 1:00-2:00 PM in Hylan 1106B:
Ken McMurdy- Regions of Reduction Type on X0(N) Part II ABSTRACT: In Part I of this talk, I discussed what it means for an elliptic curve over a local field to have bad reduction, ordinary reduction, supersingular reduction, or too-supersingular reduction. In Part II, we will use these distinctions to study the p-adic geometry of the modular curve X0(N). In particular, each point on X0(N) represents a pair (E,C) consisting of an elliptic curve E and a cyclic subgroup C of order N. Therefore it makes sense to describe points on X0(N) as "ordinary", "super singular", etc. based on the reduction type of E. The talk will feature a specific example, X0(169) over C13, which I will show has 2 ordinary components of genus 0, 2 ordinary components of genus 1, and 1 supersingular component of genus 6. The not-too-supersingular region will consist of the 4 annuli bounding (and connecting) these regions. |