PreprintCC BY 4.0arXiv
The modulo distinction problem for D*
Abstract
Let F be a nonarchimedean local field of characteristic zero and residue characteristic p. Let E be a quadratic field extension of F. Let D be the unique quaternion division algebra defined over F. Let G=GL2(E) and H=D×. This paper studies the modulo distinction problem for the pair (G,H) with ℓ≠ p, which gives a complete classification of H-distinguished representations of G, including the cases ℓ=2 and p=2. In terms of type theory, we give a complete classification of H-distinguished supercuspidal representations when p is odd.
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BibTeX
@misc{liu2026modulo,
title = {{The modulo distinction problem for D*}},
author = {Junyan Liu and Hengfei Lu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16877},
eprint = {2610.16877},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16877},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The modulo distinction problem for D*
AU - Junyan Liu
AU - Hengfei Lu
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16877
UR - https://arxiv.org/abs/2610.16877
AB - Let F be a nonarchimedean local field of characteristic zero and residue characteristic p. Let E be a quadratic field extension of F. Let D be the unique quaternion division algebra defined over F. Let G=GL_2(E) and H=D^×. This paper studies the modulo distinction problem for the pair (G,H) with ℓ≠ p, which gives a complete classification of H-distinguished representations of G, including the cases ℓ=2 and p=2. In terms of type theory, we give a complete classification of H-distinguished supercuspidal representations when p is odd.
ER -