Modularity of \GL₂( mathbbF_p)-representations over\n CM fields

2019/10/28 by Patrick B. Allen, Allen, Patrick B., Chandrashekhar Khare +3
Mathematics · Arts and Humanities · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #French Historical and Cultural Studies

paper · pdf · doi:10.48550/arxiv.1910.12986

Abstract

We prove that many representations \\ρ :\n\Gal(\K / K) \→ \GL₂( mathbbF₃),\nwhere K is a CM field, arise from modular elliptic curves. We prove similar\nresults when the prime p = 3 is replaced by p = 2 or p = 5. As a\nconsequence, we prove that a positive proportion of elliptic curves over any CM\nfield not containing a 5th root of unity are modular.\n

Citations

• Modular Elliptic Curves and Fermat's Last Theorem

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