Skip to content
DraconiticResearch
Search Sources API
181,686 studies31 sourcesUpdated 15 min ago
PreprintarXiv licencearXiv

Finite-coefficient Gersten injectivity fails in ramified mixed characteristic

  • Niels Feld
Open at sourcePDFDOICite

Abstract

Let V be a complete discrete valuation ring of mixed characteristic (0,3) in which $3$ is a uniformizer, and put A=V[[x,y]]/(3+x2−y3). We construct a nonzero class a∈ K2(A;Z/3) whose restriction to the fraction field of A is zero. Thus Gersten injectivity for algebraic K-theory with Z/3-coefficients fails for a two-dimensional ramified regular local ring. We also indicate the expected analogous construction for every odd prime. This counterexample does not contradict the integral Gersten conjecture but it rules out a naive reduction to finite coefficients.

Related

  1. A finite cover for coefficient positivity of stretched Littlewood-Richardson polynomials in the seven-row, size-thirty box
    Maseeh Ghodsi
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  2. K3 surfaces with finite automorphism group in positive characteristic
    Alexandros Vlachos
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Voevodsky motives and motives with modulus with finite coefficients in characteristic zero
    Keiho Matsumoto
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. On the singular layer for the 1-D steady Euler system with heat conductivity in a finite nozzle as the heat conduction coefficient vanishes
    Su Jiang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Classification of Finite-Dimensional Simple Novikov Algebras and Their Irreducible Bimodules in Positive Characteristic
    Dong Liu, Yufeng Pei, Limeng Xia
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryMathematical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{feld2026finitecoefficient,
  title = {{Finite-coefficient Gersten injectivity fails in ramified mixed characteristic}},
  author = {Niels Feld},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.05005},
  eprint = {2608.05005},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.05005},
}
RIS
TY  - UNPB
TI  - Finite-coefficient Gersten injectivity fails in ramified mixed characteristic
AU  - Niels Feld
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2608.05005
UR  - https://arxiv.org/abs/2608.05005
AB  - Let V be a complete discrete valuation ring of mixed characteristic (0,3) in which $3$ is a uniformizer, and put A=V[[x,y]]/(3+x^2−y^3). We construct a nonzero class a∈ K_2(A;Z/3) whose restriction to the fraction field of A is zero. Thus Gersten injectivity for algebraic K-theory with Z/3-coefficients fails for a two-dimensional ramified regular local ring. We also indicate the expected analogous construction for every odd prime. This counterexample does not contradict the integral Gersten conjecture but it rules out a naive reduction to finite coefficients.
ER  -