Structural properties of modules, quasi-projective dimension, and vanishing of Tor and Ext functors

• Grant number: 24/17809-1
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: August 02, 2025
• End date: August 01, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Victor Hugo Jorge Pérez
• Grantee: Paulo Damião Christo Martins
• Supervisor: David A Jorgensen
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: University of Texas at Arlington (UT Arlington), United States
• Associated to the scholarship: 22/12114-0 - The Tor and Ext functors: vanishing properties and related problems, BP.DR

Abstract

The study of homological dimensions of finitely generated modules over Noetherian local rings and their relationship with the vanishing of the derived functors Tor and Ext has been a topic of intense investigation in recent years. In this project, we aim to investigate the vanishing of the derived functors Tor and Ext and modules of finite quasi-projective dimension. Through this, we hope to obtain structural, homological, and geometric properties of finitely generated modules over Noetherian local rings