#### 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 $\phi :R\to S$ 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