Homological properties of the relative Frobenius morphism

Peter M. McDonald

doi:10.1090/proc/17182

Homological properties of the relative Frobenius morphism

Commutative Algebra 2026-03-12 v3

Authors: Peter M. McDonald

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Abstract

This work concerns maps of commutative noetherian local rings containing a field of positive characteristic. Given such a map $\varphi$ of finite flat dimension, the results relate homological properties of the relative Frobenius of $\varphi$ to those of the fibers of $\varphi$ . The focus is on the complete intersection property and the Gorenstein property.

Keywords

relative Frobenius morphism homological properties commutative noetherian local rings positive characteristic complete intersection property Gorenstein property finite flat dimension

Cite

@article{arxiv.2401.01880,
  title  = {Homological properties of the relative Frobenius morphism},
  author = {Peter M. McDonald},
  journal= {arXiv preprint arXiv:2401.01880},
  year   = {2026}
}

Comments

Minor edits, replaced with journal version

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