For an essentially small triangulated category
, we
introduce the notion of prime thick subcategories and define the spectrum of
, which
shares the basic properties with the spectrum of a tensor triangulated category introduced
by Balmer. We mainly focus on triangulated categories that appear in algebraic
geometry such as the derived and the singularity categories of a noetherian scheme
. We
prove that certain classes of thick subcategories are prime thick subcategories of these
triangulated categories. Furthermore, we use this result to show that certain subspaces
of
are
embedded into their spectra as topological spaces.
