An introduction to schemes

• Grant number: 19/11754-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2019
• End date: December 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Carlos Henrique Grossi Ferreira
• Grantee: Frederico Rossetto Bianchini
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main goal of the project is to introduce Grothendieck's theory of schemes as an approach to algebraic geometry. The study of classical facts involving affine and projective varieties (as well as of the corresponding pre-requisites of commutative algebra) over algebraically closed fields will serve as a motivation to the necessity of introducing schemes when it comes, say, to algebraic geometry over the ring of rational integers.