Serre’s Conjecture on 2-dimensional Galois representations
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On Serre’s Conjecture for Mod ` Galois Representations over Totally Real Fields
In 1987 Serre conjectured that any mod ` two-dimensional irreducible odd representation of the absolute Galois group of the rationals came from a modular form in a precise way. We present a generalisation of this conjecture to 2-dimensional representations of the absolute Galois group of a totally real field where ` is unramified. The hard work is in formulating an analogue of the “weight” part...
متن کاملON SERRE’S CONJECTURE FOR MOD l GALOIS REPRESENTATIONS OVER TOTALLY REAL FIELDS
In 1987 Serre conjectured that any mod l two-dimensional irreducible odd representation of the absolute Galois group of the rationals came from a modular form in a precise way. We present a generalisation of this conjecture to 2-dimensional representations of the absolute Galois group of a totally real field where l is unramified. The hard work is in formulating an analogue of the “weight” part...
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Serre’s conjecture relates two-dimensional odd irreducible characteristic p representations to modular forms. We discuss a generalization of this conjecture (due to Ash and Sinnott) to higher-dimensional Galois representations. In particular, we give a refinement of the conjecture in the case of wildly ramified Galois representations and we provide computational evidence for this refinement.
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تاریخ انتشار 2005