2 citations · 3 across the 6 of their papers we have counts for
6 papers
Atom spectra of symmetric monoidal abelian categories and classification of subcategories
Shunya Saito
We extend the classification results for torsion classes and torsion-free classes in the category of finitely generated modules over a commutative noetherian ring to suitable symme…
Classifying torsionfree classes of the category of coherent sheaves and their Serre subcategories
Shunya Saito
In this paper, we classify several subcategories of the category of coherent sheaves on a noetherian divisorial scheme (e.g. a quasi-projective scheme over a commutative noetherian…
Grothendieck monoids of extriangulated categories
Haruhisa Enomoto, Shunya Saito
We study the Grothendieck monoid (a monoid version of the Grothendieck group) of an extriangulated category, and give some results which are new even for abelian categories. First,…
The spectrum of Grothendieck monoid: classifying Serre subcategories and reconstruction theorem
Shunya Saito
The Grothendieck monoid of an exact category is a monoid version of the Grothendieck group. We use it to classify Serre subcategories of an exact category and to reconstruct the to…
A note on Grothendieck groups of periodic derived categories
Shunya Saito
We determine Grothendieck groups of periodic derived categories. In particular, we prove that the Grothendieck group of the -periodic derived category of finitely generated modu…
Tilting objects in periodic triangulated categories
Shunya Saito
A triangulated category whose suspension functor satisfies as additive functors is called an -periodic triangulated cate…