Research-On order of vanishing of characteristics elements

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On order of vanishing of characteristics elements

Speaker: Minghui Lin (Central China Normal University)
Time: Mar 31, 2022, 14:00-15:00
Location: Zoom ID 5581187360, Passcode sustech123

Abstract

Let E be an elliptic curve with either good ordinary or split multiplicative reduction at each prime above p. Coates et al has developed an algebraic K-theoretical approach of attaching characteristic elements to the Selmer group of E over a non-commutative p-adic Lie extension. In this talk, we explain how these characteristic elements "captures" the Selmer ranks of the intermediate subextensions of the said p-adic Lie extension. If time permits, we will also mention some on-going investigation of the situation (and difficulties faced) when E has good supersingular reduction at p.