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PreprintCC BY 4.0arXiv

Uniform local models of quasi-unipotent p-adic differential equations

  • Poornima Belvotagi
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Abstract

We construct uniform analytic models of quasi-unipotent differential modules over Robba rings. For modules of rank at most r and highest ramification break at most b, the inner radius of the model annulus depends only on r,b and the residue characteristic p. At each radius, the model admits a basis, possibly depending on the radius, in which the connection matrix is bounded by a constant depending only on r,b,p. Both bounds are independent of the coefficient field, and these analytic models require no coefficient extension. A prescribed absolute Frobenius structure extends to such a bounded model with the same radius and connection bound. After a finite coefficient extension, we also realize quasi-constant modules, which carry the finite local monodromy, as differential direct summands of sums of pushforwards of rank-one modules, with uniformly bounded cover degrees and highest breaks of the inducing modules.

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Cite

BibTeXRIS
BibTeX
@misc{belvotagi2026uniform,
  title = {{Uniform local models of quasi-unipotent $p$-adic differential equations}},
  author = {Poornima Belvotagi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36130},
  eprint = {2610.36130},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36130},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Uniform local models of quasi-unipotent p-adic differential equations
AU  - Poornima Belvotagi
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.36130
UR  - https://arxiv.org/abs/2610.36130
AB  - We construct uniform analytic models of quasi-unipotent differential modules over Robba rings. For modules of rank at most r and highest ramification break at most b, the inner radius of the model annulus depends only on r,b and the residue characteristic p. At each radius, the model admits a basis, possibly depending on the radius, in which the connection matrix is bounded by a constant depending only on r,b,p. Both bounds are independent of the coefficient field, and these analytic models require no coefficient extension. A prescribed absolute Frobenius structure extends to such a bounded model with the same radius and connection bound. After a finite coefficient extension, we also realize quasi-constant modules, which carry the finite local monodromy, as differential direct summands of sums of pushforwards of rank-one modules, with uniformly bounded cover degrees and highest breaks of the inducing modules.
ER  -