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| Author(s): |
Paulo Damião Christo Martins
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2023-02-15 |
| Examining board members: |
Victor Hugo Jorge Pérez;
Kostiantyn Iusenko;
Daniel Levcovitz;
Rainelly Cunha de Medeiros
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| Advisor: | Victor Hugo Jorge Pérez |
| Abstract | |
The study of free resolutions of modules over a commutative ring is an important tool to obtain properties of the module that we want to investigate. In this work, using minimal free resolutions, we will study the Betti numbers of finitelly generated modules over a Noetherian local ring. We will present applications of such invariants in Commutative Algebra, open problems and recent results related to the topic. Also, we will introduce a series of Homological Algebra tools that we will apply throughout this text, such as the derived functors Tor and Ext and the Koszul Complex. (AU) | |
| FAPESP's process: | 21/00737-0 - About homological algebra of modules, the Tor and Ext functors and conjectures |
| Grantee: | Paulo Damião Christo Martins |
| Support Opportunities: | Scholarships in Brazil - Master |