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- W4313679803 abstract "For a genus $2$ curve $C$ over $mathbb{Q}$ whose Jacobian $A$ admits only trivial geometric endomorphisms, Serre's open image theorem for abelian surfaces asserts that there are only finitely many primes $ell$ for which the Galois action on $ell$-torsion points of $A$ is not maximal. Building on work of Dieulefait, we give a practical algorithm to compute this finite set. The key inputs are Mitchell's classification of maximal subgroups of $mathrm{PSp_4}(mathbb{F}_ell)$, sampling of the characteristic polynomials of Frobenius, and the Khare--Wintenberger modularity theorem. The algorithm has been submitted for integration into Sage, executed on all of the genus~$2$ curves with trivial endomorphism ring in the LMFDB, and the results incorporated into the homepage of each such curve." @default.
- W4313679803 created "2023-01-08" @default.
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- W4313679803 date "2023-01-05" @default.
- W4313679803 modified "2023-10-12" @default.
- W4313679803 title "Computing nonsurjective primes associated to Galois representations of genus $2$ curves" @default.
- W4313679803 doi "https://doi.org/10.48550/arxiv.2301.02222" @default.
- W4313679803 hasPublicationYear "2023" @default.
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