Exceptional complete intersection maps of local rings

Srikanth B. Iyengar, Janina C. Letz, Jian Liu and Josh Pollitz

Vol. 318 (2022), No. 2, 275–293

DOI: 10.2140/pjm.2022.318.275

Abstract

This work concerns surjective maps $\phi :R\to S$ of commutative noetherian local rings with kernel generated by a regular sequence that is part of a minimal generating set for the maximal ideal of $R$. The main result provides criteria for detecting such exceptional complete intersection maps in terms of the lattices of thick subcategories of the derived category of complexes of finite length homology. A key input is a characterization of such maps in terms of the truncated Atiyah class of $\phi$.

Keywords

exceptional complete intersection, Hochschild cohomology, truncated Atiyah class, thick subcategory

Mathematical Subject Classification

Primary: 13B10

Secondary: 13D03, 13D09

Milestones

Received: 15 July 2021

Revised: 22 February 2022

Accepted: 16 April 2022

Published: 20 August 2022