Shunya SAITO

Publications

1. A note on Grothendieck groups of periodic derived categories, J. Algebra 609 (2022), 552--566. [journal] [arXiv:2112.09874]

2. Tilting theory for periodic triangulated categories, Math. Z. 304, 47 (2023).  [journal] [arXiv:2011.14096]

3. When are KE-closed subcategories torsion-free classes? (joint work with Toshinori Kobayashi), Math. Z. 307, 65 (2024). [journal] [arXiv:2309.01044]

4. The spectrum of Grothendieck monoid: classifying Serre subcategories and reconstruction theorem, J. Algebra 658, (2024), 365--414. [journal] [arXiv:2206.15271]

5. Classifying torsionfree classes of the category of coherent sheaves and their Serre subcategories, J. Pure Appl. Algebra 229, (2025), no. 1, Paper No. 107799. [journal] [arXiv:2304.06918]

Preprints

1. Grothendieck monoids of extriangulated categories. (joint work with Haruhisa Enomoto) [arXiv:2208.02928]

2. Classifying KE-closed subcategories over a commutative noetherian ring. (joint work with Toshinori Kobayashi) [arXiv:2509.05767]

• ヘンゼル環と Krull-Schmidt 圏 (written in japanese) [pdf]
  Krull-Schmidt圏(=直既約分解の一意性が成立する加法圏)・半完全環・ヘンゼル環の関係をまとめました．とくにCohen-Macaulay表現論などでファクトにされる完備局所可換環上の加群圏はKrull-Schmidt圏になることを示しています．前提知識は少なめですが，有限次元代数の表現論への慣れは必要な気がします．

• DG categories [pdf]
  It is a part of my master's thesis. This note contains basic materials on DG categories and aims to prove the derived Morita theorem due to Keller, which yields a triangle equivalence between a certain triangulated category and the derived category of a DG category. This note does not cover homotopical stuff on DG categories.

Upcoming talks

• ------ (December 12)
  Conference Talk, Tokyo-Seoul Conference in Mathematics 2025: Enumerative Geometry and Representation Theory, The University of Tokyo 

• Classifying KE-closed subcategories over a commutative noetherian ring (December 16, 2025)
  Conference Talk, Spectrums in Representation Theory of Algebras and Related Topics, Osaka Metropolitan University

Past talks

1. 周期三角圏上の傾理論 (February 24, 2021) [slide]
   Seminar Talk, Tokyo-Nagoya Algebra Seminar, Online

2. Tilting objects in periodic triangulated categories (June 27, 2021) [slide]
   Conference Talk, Algebraic Lie Theory and Representation Theory 2021 (ALTReT 2021), Online

3. Tilting theory for periodic triangulated categories (September 8, 2021) [slide]
   Conference Talk, The 53rd Symposium on Ring Theory and Representation Theory, Online (Yamaguchi University)

4. 周期導来圏と傾理論 (February 9, 2022) [slide]
   Conference Talk, Mathsci Freshman Seminar 2022, Online (Kyushu University)

5. The spectrum of Grothendieck monoid: a new approach to classify Serre subcategories (July 22, 2022) [slide]
   Seminar Talk, Suita Representation Seminar, Online

6. The spectrum of Grothendieck monoid (September 7, 2022) [slide]
   Conference Talk, The 54th Symposium on Ring Theory and Representation Theory, Saitama University

7. The spectrum of Grothendieck monoid (March 28, 2023) [slide]
   Conference Talk, 27th Conference on Algebra for Young Researchers in Japan, University of Tsukuba

8. Classifying torsionfree classes of the category of coherent sheaves and their Serre subcategories (May 26, 2023) [slide]
   Seminar Talk, Sugimoto Algebra Seminar, Osaka Metropolitan University

9. Classifying Serre subcategories of the category of maximal Cohen-Macaulay modules (July 6, 2023) [slide]
   Conference Talk, The 34th Commutative Algebra Seminar, Kitami Institute of Technology

10. Classifying Serre subcategories of the category of maximal Cohen-Macaulay modules (August 15, 2023) [slide]
    Conference Talk, The 9th China-Japan-Korea International Conference on Ring and Module Theory, Incheon National University

11. Classifying several subcategories of the category of maximal Cohen-Macaulay modules (September 6, 2023) [slide]
    Conference Talk, The 55th Symposium on Ring Theory and Representation Theory, Osaka Metropolitan University

12. Classifying torsionfree classes of the category of coherent sheaves and their Serre subcategories (December 22, 2023)  [slide]
    Conference Talk, McKay correspondence, Tilting theory and related topics, Kavli IPMU

13. Classifications of subcategories of exact categories (June 18, 2024)  [slide]
    Mini workshop, Classifications of subcategories of abelian and triangulated categories, Tokyo University of Agriculture and Technology

14. Classifying KE-closed subcategories (June 28, 2024)  [slide]
    Seminar Talk, Tokyo-Nagoya Algebra Seminar, Online

15. Tilting theory for 1-dimensional Gorenstein rings (August 23, 2024)
    Lecture, The 19th Summer School on Commutative algebra, The University of Tokyo

16. Torsion-free classes of smooth projective curves of genus 0 and 1  (September 18, 2024)  [slide]
    Conference Talk,  The 56th Symposium on Ring Theory and Representation Theory, Tokyo Gakugei University

17. Classifying KE-closed subcategories over a commutative noetherian ring (February 21, 2025)  [slide]
    Conference Talk, Perspectives in Tilting Theory and Related Topics, Kyoto University

18. Classifying KE-closed subcategories over a commutative noetherian ring (July 5, 2025) [slide]
    Seminar Talk, Yamaguchi Algebra Seminar, Yamaguchi University

19. Classifying KE-closed subcategories over a commutative noetherian ring (September 10, 2025) [slide]
    Conference Talk, The 57th Symposium on Ring Theory and Representation Theory, Okayama University of Science

• 明治大学 (2025 春, 工学部 複素関数論) [link]

• 愛知学院大学 (2023 秋, 文系教養 線形代数) [link]

• 愛知学院大学 (2023 春, 文系教養 微積分) [link]