Exceptional complete intersection maps of local rings

Abstract

This work concerns surjective maps $\ddot{I}†:R\to S$ 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 $\ddot{I}†$.

16 pages; added a missing hypothesis to Lemma 2.8, and minor changes to the proofs of Theorems 3.4 and 5.6. To appear in the Pacific Journal of Mathematics