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PreprintarXiv licencearXiv

Reductions of GL2(ℚpf)-Banach spaces of slopes in (0,1)

  • Eknath Ghate
  • Shivansh Pandey
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Abstract

Let p be an odd prime and f ≥ 1. We consider a p-adic locally algebraic GL2(ℚpf)-representation attached to a tuple of f weights k=(ki) for 0 ≤ i ≤ f−1 and a p-adic integer ap with valuation in (0,1). We give conditions under which the irreducible quotients of the subquotients in a filtration on the reduction mod p of the natural integral structure on this space are supercuspidal. We also check that for small k and f the integral structure is a lattice so that the mod p reduction is nonzero.

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Cite

BibTeXRIS
BibTeX
@misc{ghate2026reductions,
  title = {{Reductions of $\mathrmGL_2(\mathbb Q_p^f)$-Banach spaces of slopes in $(0,1)$}},
  author = {Eknath Ghate and Shivansh Pandey},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.02654},
  eprint = {2605.02654},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.02654},
}
RIS
TY  - UNPB
TI  - Reductions of GL_2(ℚ_p^f)-Banach spaces of slopes in (0,1)
AU  - Eknath Ghate
AU  - Shivansh Pandey
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2605.02654
UR  - https://arxiv.org/abs/2605.02654
AB  - Let p be an odd prime and f ≥ 1. We consider a p-adic locally algebraic GL_2(ℚ_p^f)-representation attached to a tuple of f weights k=(k_i) for 0 ≤ i ≤ f−1 and a p-adic integer a_p with valuation in (0,1). We give conditions under which the irreducible quotients of the subquotients in a filtration on the reduction mod p of the natural integral structure on this space are supercuspidal. We also check that for small k and f the integral structure is a lattice so that the mod p reduction is nonzero.
ER  -