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- W4300461176 abstract "Let $K$ be a number field, $n>4$ an integer, $f(x)$ an irreducible polynomial over $K$ of degree $n$, whose Galois group is either the full symmetric group $S_n$ or the alternating group $A_n$. Suppose $C:y^2=f(x)$ is the corresponding hyperelliptic curve and $J$ its jacobian defined over $K$. For each prime $ell$ we write $V_{ell}(J)$ for the $Q_{ell}$-Tate module of $J$ and $e_{ell}$ for the Riemann form on $V_{ell}(J)$ attached to the theta divisor. (Here $Q_{ell}$ is the field of $ell$-adic numbers.) We write $sp(V_{ell}(J))$ for the $Q_{ell}$-Lie algebra of the symplectic group of $e_{ell}$. We write $g_{ell}$ for the Lie algebra of the image of the Galois group $Gal(K)$ of $K$ in $Aut(V_{ell}(J))$. We prove that $g_{ell}$ coincides with the direct sum $Q_{ell}I oplus sp(V_{ell}(J))$ where $I$ is the identity operator." @default.
- W4300461176 created "2022-10-03" @default.
- W4300461176 creator A5066186961 @default.
- W4300461176 date "2001-09-03" @default.
- W4300461176 modified "2023-09-26" @default.
- W4300461176 title "Very simple 2-adic representations and hyperelliptic jacobians" @default.
- W4300461176 doi "https://doi.org/10.48550/arxiv.math/0109014" @default.
- W4300461176 hasPublicationYear "2001" @default.
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