Vanishing of Ext and Tor, and free modules.

• Grant number: 23/15733-5
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: August 17, 2024
• End date: August 16, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Victor Hugo Jorge Pérez
• Grantee: Victor Daniel Mendoza Rubio
• Supervisor: Roger Allen Wiegand
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: University of Nebraska-Lincoln (UNL), United States
• Associated to the scholarship: 22/03372-5 - On the Auslander-Reiten conjecture, BP.DR

Abstract

This project aims to investigate the implications of the vanishing of Ext and Tor. One of its objectives is to establish criteria for the freeness of a module over a Noetherian local ring through the vanishing of specific Ext or Tor modules. Special attention is dedicated to cases where the Hom or the tensor product of two particular modules has some finite homological dimension.