Let be a commutative noetherian ring. Denote by the derived category of cochain complexes of finitely generated -modules with for . Then has the structure of a tensor triangulated category with tensor product and unit object . In this paper, we study thick tensor ideals of , i.e., thick subcategories closed under the tensor action by each object in , and investigate the Balmer spectrum of , i.e., the set of prime thick tensor ideals of . First, we give a complete classification of the thick tensor ideals of generated by bounded complexes, establishing a generalized version of the Hopkins–Neeman smash nilpotence theorem. Then, we define a pair of maps between the Balmer spectrum and the Zariski spectrum , and study their topological properties. After that, we compare several classes of thick tensor ideals of , relating them to specialization-closed subsets of and Thomason subsets of , and construct a counterexample to a conjecture of Balmer. Finally, we explore thick tensor ideals of in the case where is a discrete valuation ring.
"Thick tensor ideals of right bounded derived categories." Algebra Number Theory 11 (7) 1677 - 1738, 2017. https://doi.org/10.2140/ant.2017.11.1677