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

We define a duality operation connecting closure operations, interior and test ideals, describe how the acts on common constructions such as trace, torsion, tight integral closures, divisible submodules. This generalizes relationship between demonstrated by Epstein Schwede (2014) allows us to extend commonly used results ideals operations those above.