Vol. 318, No. 2, 2022

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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
Abstract

This work concerns surjective maps φ: R 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 φ.

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
Authors
Srikanth B. Iyengar
Department of Mathematics
University of Utah
Salt Lake City, UT
United States
Janina C. Letz
Faculty of Mathematics
Bielefeld University
Bielefeld
Germany
Jian Liu
School of Mathematical Sciences
Shanghai Jiao Tong University
Shanghai
China
Josh Pollitz
Department of Mathematics
University of Utah
Salt Lake City, UT
United States