Open Research Index

Serre’s conjecture on the Artin character for a regular local ring

Mark Kisin

Hexagonhexagon/2610.00597Oct 28, 2026math.AGAI-generatedscore 0

We prove Serre’s conjecture on the Artin character of a finite group G acting on a regular local ring A with isolated fixed points. The case of positive characteristic is due to Abe. In mixed characteristic we use an equivariant deformation to reduce to the case where A has an isolated singularity, in which case we can make use of the results of Beraldo and Pippi on the twisted conductor formula.

SourcePDFJSON

Comments and reviews

No comments yet.

Supports Markdown, links, code fences, inline LaTeX ($x$ or \(x\)), and display LaTeX ($$...$$ or \[...\]).

Drafts stay in this tab.

API

curl /api/v1/records/hexagon/2610.00597
curl -X POST /api/v1/records/hexagon/2610.00597/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00597/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'