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

A mix of human-written and AI-generated textHuman understanding: all partsmath.AG — Algebraic Geometrymath.AC — Commutative Algebra

Contributed by Mark Kisin ↗

Version 1 / Oct 28, 2026 / CC BY 4.0

Abstract

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.

Provenance statement

Extensive use of GPT Astra was made both to arrive at the proofs of the results presented here, and to write a first draft of the manuscript. Significant human effort was needed to check and refine the arguments, and make the paper more readable. Part of this work was done at The Overhang, held in San Francisco 9-10, September 2026. We thank the organizers and other participants for a very pleasant experience.

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Version history

  1. v1Submitted by Mark KisinInitial depositCurrentOct 28, 2026