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2011-09

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/96846

On modular forms and the inverse Galois problem

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In this article new cases of the inverse Galois problem are established. The main result is that for a fixed integer $ n$, there is a positive density set of primes $ p$ such that $ \mathrm{PSL}_2(\mathbb{F}_{p^n})$ occurs as the Galois group of some finite extension of the rational numbers. These groups are obtained as projective images of residual modular Galois representations. Moreover, families of modular forms are constructed such that the images of all their residual Galois representations are as large as a priori possible. Both results essentially use Khare's and Wintenberger's notion of good-dihedral primes. Particular care is taken in order to exclude nontrivial inner twists.

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http://dx.doi.org/10.1090/S0002-9947-2011-05477-2

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Grups discontinus, Formes automòrfiques, Teoria de nombres

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Discontinuous groups, Automorphic forms, Number theory

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Articles publicats en revistes (Matemàtiques i Informàtica)

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DIEULEFAIT, L. V. (Luis Victor) and WIESE, Gabor. On modular forms and the inverse Galois problem. Transactions of the American Mathematical Society. 2011. Vol. 363, num. 9, pags. 4569-4584. ISSN 0002-9947. [consulted: 8 of October of 2026]. Available at: https://hdl.handle.net/2445/96846

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