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Displaying similar documents to “On Galois representations arising from towers of coverings of P1 ... .”

On the equation a³ + b³ⁿ = c²

Michael A. Bennett, Imin Chen, Sander R. Dahmen, Soroosh Yazdani (2014)

Acta Arithmetica

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We study coprime integer solutions to the equation a³ + b³ⁿ = c² using Galois representations and modular forms. This case represents perhaps the last natural family of generalized Fermat equations descended from spherical cases which is amenable to resolution using the so-called modular method. Our techniques involve an elaborate combination of ingredients, ranging from ℚ-curves and a delicate multi-Frey approach, to appeal to intricate image of inertia arguments.

An infinite ferm in the universal deformation space of Galois representations.

B. Mazur (1997)

Collectanea Mathematica

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I hope this article will be helpful to people who might want a quick overview of how modular representations fit into the theory of deformations of Galois representations. There is also a more specific aim: to sketch a construction of a point-set topological'' configuration (the image of an infinite fern'') which emerges from consideration of modular representations in the universal deformation space of all Galois representations. This is a configuration hinted previously, but now, thanks...