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Showing 1 to 5 of 5 for “"Serre's Conjecture"”.
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Proven Cases of a Generalization of Serre's Conjecture
In the 1970's Serre conjectured a correspondence between modular forms and two-dimensional Galois representations. Ash, Doud, and Pollack have extended this conjecture to a correspondence between Hecke eigenclasses in arithmetic cohomology and n-dimensional Galois representations. We present some …
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Explicit Computations Supporting a Generalization of Serre's Conjecture
Serre's conjecture on the modularity of Galois representations makes a connection between two-dimensional Galois representations and modular forms. A conjecture by Ash, Doud, and Pollack generalizes Serre's to higher-dimensional Galois representations. In this paper we discuss an explicit …
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Emerton-Gee Stacks, Serre Weights, and Breuil-Mézard Conjectures for GSp_4
… an GSp_4-analogue of the Breuil-Mézard conjecture for tamely potentially crystalline deformation rings, the weight part of Serre's conjecture formulated by Gee-Herzig-Savitt for global Galois representations valued in GSp_4 satisfying Taylor--Wiles conditions, and a modularity lifting …
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Lifting Galois Representations in a Conjecture of Figueiredo
<p>In 1987, Jean-Pierre Serre gave a conjecture on the correspondence between degree 2 odd irreducible representations of the absolute Galois group of Q and modular forms. Letting M be an imaginary quadratic field, L.M. Figueiredo gave a related conjecture concerning degree 2 irreducible …