About homological algebra of modules, the Tor and Ext functors and conjectures

• Grant number: 21/00737-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2021
• End date: February 28, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Victor Hugo Jorge Pérez
• Grantee: Paulo Damião Christo Martins
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

We will present here a research project, extremely broad in commutative algebra and homological algebra, which will be investigated over a two-year master's degree. This project is based on homological algebra theory such as Ext and Tor funkers, local module cohomology. But explicitly, the objective is to explore the structure and algebraic, homological, arithmetic and geometric properties of finitely generated modules. One of the goals is to study special classes of modules, the depth formula for tensor products, the Auslander-Reiten conjecture, and the impact of finitude of various homological dimensions.In turn, we also propose to investigate the Buchsbaum-Eisenbud-Horrocks conjecture which has been an active topic of investigation. Especially, the "total rank" conjecture that recently had a positive response from Mark Walker. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MARTINS, Paulo Damião Christo. Betti numbers: applications and related problems.. 2023. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.