PreprintarXiv licencearXiv
On the abundance of rigid meromorphic cocycles for quadratic forms in four variables
Abstract
Let (V,q) be an anisotropic quadratic space of dimension $4$ over the rationals and let p be a prime such that the local quadratic space V⊗ ℚp is the orthogonal direct sum of two hyperbolic planes. We show that the group of p-adic rigid meromorphic cocycles attached to V has infinite rank. A key ingredient in the proof is the computation of the group of invertible rigid analytic functions on products of certain rigid analytic subspaces of the projective line such as the p-adic upper half-plane.
Related
- Counting solutions to quadratic forms in eight prime variables of off-diagonal rank $3$
- Translation invariant quadratic forms in $8$ variables and dense sets of primes
- A pencil of quadratic forms in nine variables with no member of Witt index four
- Cocycles on Tiling Spaces
- Periodic data conjugacy for diffeomorphism cocycles
BibTeX
@misc{gehrmann2026abundance,
title = {{On the abundance of rigid meromorphic cocycles for quadratic forms in four variables}},
author = {Lennart Gehrmann and Sören Sprehe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24309},
eprint = {2609.24309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24309},
}
RIS
TY - UNPB
TI - On the abundance of rigid meromorphic cocycles for quadratic forms in four variables
AU - Lennart Gehrmann
AU - Sören Sprehe
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24309
UR - https://arxiv.org/abs/2609.24309
AB - Let (V,q) be an anisotropic quadratic space of dimension $4$ over the rationals and let p be a prime such that the local quadratic space V⊗ ℚ_p is the orthogonal direct sum of two hyperbolic planes. We show that the group of p-adic rigid meromorphic cocycles attached to V has infinite rank. A key ingredient in the proof is the computation of the group of invertible rigid analytic functions on products of certain rigid analytic subspaces of the projective line such as the p-adic upper half-plane.
ER -