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- W202737495 abstract "The image of a complex conjugation by a two-dimensional representation of (mathrm{Gal}(overline{mathbb {Q}}/mathbb {Q})) in characteristic 2 can be trivial or a non-trivial element of order 2. Since such a representation comes from a modular form f, we attempt to study such an alternative purely in terms of f. The component group of the real points of the modular Jacobian J 1(N) plays a role in this question. We give an elementary description of that group. Our method to obtain such a description applies to determine the component group at infinity of the Jacobian of modular curves over (mathbb {R}) attached to any subgroup of finite index of (mathrm{SL}_{2}(mathbb {Z})). We show that such a group is always “Eisenstein”. We derive a few consequences of this last fact for Galois representations and modular parametrisations." @default.
- W202737495 created "2016-06-24" @default.
- W202737495 creator A5048016841 @default.
- W202737495 date "2014-01-01" @default.
- W202737495 modified "2023-09-26" @default.
- W202737495 title "Formes modulaires modulo 2 et composantes réelles de jacobiennes modulaires" @default.
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- W202737495 doi "https://doi.org/10.1007/978-3-319-03847-6_8" @default.
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