The p-adic local Langlands for dihedral Galois representations.


Jeehoon Park

11:30:00 - 12:20:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

The goal of this talk is to construct the p-adic Local Langlands correspondence for GL_2 for the 2-dimensional irreducible dihedral p-adic Galois representations. P. Colmez constructed such a correspondence for any p-adic Galois representation via the theory of (\phi,\Gamma)-modules. Our method is completely different from his and we use more representation theoretic technic not using any (\phi,\Gamma)-modules. We do this by constructing a $p$-adic theta correspondence between p-adic characters of a quadratic extension field E of Q_p and admissible p-adic Banach representations of GL_2(Q_p).

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