Banach-Hecke algebras and p-adic Galois Representations

Details Banach-Hecke algebras and p-adic Galois Representations Banach-Hecke algebras and p-adic Galois Representations

2005-10-30

arxiv.org/abs/math/0510661v1

Mathematics

Number Theory

Dedicated to John Coates on his 60th birthday

Scientific paper

We take some initial steps towards illuminating the (hypothetical) $p$-adic local Langlands functoriality principle relating Galois representations of a $p$-adic field $L$ and admissible unitary Banach space representations of $G(L)$ when $G$ is a split reductive group over $L$. The outline of our work is derived from Breuil's remarkable insights into the nature of the correspondence between 2-dimensional crystalline Galois representations of the Galois group of $\Qdss_p$ and Banach space representations of $GL_{2}(\Qdss_p)$.

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