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arXiv · 1402.4082

A note on L-packets and abelian varieties over local fields

Jeff Achter·Clifton Cunningham
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Abstract

A polarized abelian variety (X,\lambda) of dimension g over a local field K determines an admissible representation of GSpin_{2g+1}(K). We show that the restriction of this representation to Spin_{2g+1}(K) is reducible if and only if X is isogenous to its twist by the quadratic unramified extension of K. When g=1 and K = Q_p, we recover the well-known fact that the admissible GL_2(K) representation attached to an elliptic curve E is reducible upon restriction to SL_2(K) if and only if E has supersingular reduction.

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Jeff Achter, Clifton Cunningham. 2014-02-17. A note on L-packets and abelian varieties over local fields. https://doi.org/10.2140/pjm.2015.273.395

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