English

Non-reduced valuation rings and descent for smooth blowup squares

Algebraic Geometry 2024-01-08 v1

Abstract

We consider a class of non-reduced valuation rings, known in the literature as chain rings. We observe that the Grothendieck topology generated by the Zariski topology and smooth blowup squares is exactly the topology which has chain rings for its local rings, and that sheaves for this topology are \emph{not} characterised by excision for smooth blowup squares.

Keywords

Cite

@article{arxiv.2401.02706,
  title  = {Non-reduced valuation rings and descent for smooth blowup squares},
  author = {Shane Kelly},
  journal= {arXiv preprint arXiv:2401.02706},
  year   = {2024}
}

Comments

13 pages