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- W176261004 abstract "In my earlier paper [H07] and in my talk at the workshop on “Arithmetic Algebraic Geometry” at RIMS in September 2006, we made explicit a conjectural formula of the L-invariant of symmetric powers of a Tate curve over a totally real field (generalizing the conjecture of Mazur-Tate-Teitelbaum, which is now a theorem of Greenberg-Stevens). In this paper, we prove the formula for Greenberg’s L-invariant when the symmetric power is of adjoint type, assuming a standard conjecture (see Conjecture 0.1) on the ring structure of a Galois deformation ring of the symmetric powers. Let p be an odd prime and F be a totally real field of degree d b. Write Fj = Fpj for the pj-adic completion of F and qj ∈ F× j with j ≤ b for the Tate period of E/Fj . Put Qj = NFpj /Qp(qj). When b = 0, as a convention, we assume that E/F has good ordinary reduction at every p-adic place of F . We assume throughout the paper that E does not have complex" @default.
- W176261004 created "2016-06-24" @default.
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- W176261004 date "2009-01-01" @default.
- W176261004 modified "2023-09-27" @default.
- W176261004 title "L-Invariant of the Symmetric Powers of Tate Curves" @default.
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