Finite functorial conditions of subcategories of modules of finite projective dimension

• Grant number: 24/21136-2
• Support Opportunities: Scholarships abroad - Research
• Start date: September 01, 2025
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Flavio Ulhoa Coelho
• Grantee: Flavio Ulhoa Coelho
• Host Investigator: Manuel Saorin Castaño
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Universidad de Murcia, Spain

Abstract

For a given algebra $\Lambda$, denote by mod$\Lambda$ the category of the finitely generated right $\Lambda$-modules and by $\mathcal{P}^{<\infty}$(\mbox{mod}$\Lambda)$ the subcategory of the $\Lambda$-modules of finite projective dimensions. The aim of our work is to extend the number of classes of algebras such that $\mathcal{P}^{<\infty}$(\mbox{mod}$\Lambda)$ satisfies the property called contravariantly finite. The importance of this study is that if such property holds, then the algebra will satisfy one of the most intriguing homological conjectures, the so-called finitistic dimension conjecture. We shall focus in recent developed techniques to reach the aims propsed above.