Title: Adjoint Selmer groups and cyclicity I
Speaker: Adjoint Selmer groups and cyclicity I (UCLA)
Time: 2019-6-24, 15:00-17:00
Place: MCM;610
Abstract: For a given elliptic cusp form f, we have a 2-dimensional p-adic Galois representation r with coefficients in a p-adic integer ring. Having r act on SL(2)-Lie algebra by adjoint (conjugate action), we get a 3-dimensional representation Ad. We describe the formula of the order of the p-adic arithmetic cohomology group Sel(Ad) (called the adjoint Selmer group) via the L-value L(1,Ad)=L(1,Ad(f)) and explore the question when the Selmer group is cyclic (having one generator) over the coefficient ring?
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