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Vanishing of Ext and Tor, and free modules.

Grant number: 23/15733-5
Support Opportunities:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): August 01, 2024
Effective date (End): July 31, 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
Research place: 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.

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