Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 29 min ago
PreprintCC BY 4.0arXiv

Coherence and the Hilbert-syzygy identity for power series over valuation domains

  • Mohamed Amine Aouichaoui
  • Adam Jones
  • Yiding Wang
Open at sourcePDFDOICite

Abstract

Let V be a complete valuation domain of rank 1, and let Γ be its value group. We investigate the power series ring V[[t]], and finally answer the long standing question of when this ring is coherent. Specifically, we prove that it is coherent if and only if V is almost maximal, and either Γ= ℝ or Γ is discrete. Furthermore, we demonstrate that the weak Hilbert-syzygy identity w. dim V [[X]] = w. dim V + 1 holds if and only if V[[X]] is a coherent ring.

Related

  1. The tensor triangular geometry of valuation domains
    Tobias Barthel, Drew Heard, Beren Sanders +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  2. Hermitian Clifford Analysis on Euclidean Domains with Smooth and Fractal Boundaries: A Survey of Matrix Cauchy and Hilbert Transforms, Boundary Value Problems, Helmholtz-Type Dirac Operators and Duality
    Ricardo Abreu-Blaya, Juan Bory-Reyes, Carlos Daniel Tamayo-Castro
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Auslander-type grade conditions and subcategories related to syzygy modules
    Yuya Otake
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Syzygy Transformations of Cluster Characters and Geometric Twists
    Jiarui Fei
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Syzygy and Adjoint Matroids
    Jaeho Shin
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{aouichaoui2026coherence,
  title = {{Coherence and the Hilbert-syzygy identity for power series over valuation domains}},
  author = {Mohamed Amine Aouichaoui and Adam Jones and Yiding Wang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05246},
  eprint = {2611.05246},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05246},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Coherence and the Hilbert-syzygy identity for power series over valuation domains
AU  - Mohamed Amine Aouichaoui
AU  - Adam Jones
AU  - Yiding Wang
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05246
UR  - https://arxiv.org/abs/2611.05246
AB  - Let V be a complete valuation domain of rank 1, and let Γ be its value group. We investigate the power series ring V[[t]], and finally answer the long standing question of when this ring is coherent. Specifically, we prove that it is coherent if and only if V is almost maximal, and either Γ= ℝ or Γ is discrete. Furthermore, we demonstrate that the weak Hilbert-syzygy identity w. dim V [[X]] = w. dim V + 1 holds if and only if V[[X]] is a coherent ring.
ER  -